<PAGE>
 
                                                                    EXHIBIT 10.5
                                                                                
                              SECOND AMENDMENT TO
                              -------------------
                  THIRD AMENDED AND RESTATED CREDIT AGREEMENT
                  -------------------------------------------

     THIS SECOND AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT (the
"Amendment") dated as of September 30, 1998 by and among NEW CENTURY MORTGAGE
CORPORATION, a California corporation (the "Company"), the lenders party to the
Credit Agreement referred to below (collectively, the "Lenders" and
individually, a "Lender"), and U.S. BANK NATIONAL ASSOCIATION, a national
banking association, in its capacity as agent for the Lenders (in such capacity,
together with any successor agents appointed thereunder, the "Agent").

     WITNESSETH THAT:

     WHEREAS, the Company, the Lenders and the Agent are parties to a Third
Amended and Restated Credit Agreement dated as of May 29, 1998 as amended by a
First Amendment to Third Amended and Restated Credit Agreement dated as of July
27, 1998 (as so amended, the "Credit Agreement"), pursuant to which the Lenders
provide the Company with a revolving mortgage warehousing credit facility; and

     WHEREAS, the Company and the Lenders have agreed to amend the Credit
Agreement upon the terms and conditions herein set forth;

     NOW, THEREFORE, for value received, the receipt and sufficiency of which
are hereby acknowledged, the Company and the Lenders agree as follows:

         Certain Defined Terms.  Each capitalized term used herein without being
         --------------------- 
defined herein that is defined in the Credit Agreement shall have the meaning
given to it therein.

     2.  Amendments to Credit Agreement.  The Credit Agreement is hereby
         ------------------------------                                       
amended as follows:

         (a) Definitions.  Section 1.01 is hereby amended by adding the
             -----------                                               
     following new definitions in correct alphabetical order:

         "REO":  real property acquired by the Company as a result of the
     foreclosure of a Mortgage Loan.

         "REO Sub":  New Century REO Corp., a California corporation.
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<PAGE>
 
         "Salomon REO Agreement":  a letter agreement dated as of September __,
          ---------------------
     1998 by and between the Company and SBRC, together with a secured
     promissory note dated as of September_______, 1998 (the "Secured Promissory
     Note") and a pledge agreement dated as of September_______ , 1998 (the "REO
     Subsidiary Pledge Agreement"), pursuant to which SBRC provides financing to
     the Company with respect to REO transferred to REO Sub by the Company, as
     the same may be amended, supplemented, restated or otherwise modified in
     accordance with this Agreement and in effect from time to time.

          (b)  Indebtedness.  Section 4.08 is hereby amended by deleting the
               ------------
     word "and" at the end of subsection (f) thereof, deleting the period at the
     end of subsection (g) thereof and inserting a semicolon followed by the
     word "and" therefor, and inserting the following new subsection (h) at the
     end thereof:

               (h)  Indebtedness incurred by the Company in connection with the
               Salomon REO Agreement in an aggregate amount not to exceed
               $3,000,000.

          (c)  Liens.  Section 4.09 is hereby amended by deleting the word "and"
               -----                                                            
     at the end of subsection (g) thereof, deleting the period at the end of
     subsection (h) thereof and inserting a semicolon followed by the word "and"
     therefor, and inserting the following new subsection (i) at the end
     thereof:

               (i)  a pledge of the stock of REO Sub to SBRC pursuant to the
               Salomon REO Agreement.

          (d)  Restriction on Fundamental Changes.  Section 4.12 is hereby
               ----------------------------------                         
     amended by deleting the word "and" at the end of subsection (a) thereof,
     deleting the period at the end of subsection (b) thereof and inserting a
     semicolon followed by the word "and" therefor, and inserting the following
     new subsection (c) at the end thereof:

               (c) The Company may transfer REO with a book value not to exceed
               $6,000,000 at any time to REO Sub, provided that the Agent's
               security interest, if any, for the benefit of the Lenders in the
               related Mortgage Loan has been released in accordance with the
               Pledge and Security Agreement and no Eligible Servicing
               Receivables (as defined in Exhibit E) relating thereto are
               included in the Borrowing Base.
 
          (e)  Subsidiaries.  Section 4.17 is hereby amended in its entirety to
               ------------
     read as follows:

               4.17  Subsidiaries.  (a) The Company will not create or acquire
                     ------------                                              
               any Subsidiaries other than REO Sub, and (b) NCFC will not 
<PAGE>
 
               create or acquire any Subsidiaries other than (i) the Company,
               (ii) Subsidiaries engaged solely in any business involving the
               origination, acquisition, servicing and sale of consumer
               obligations, and (iii) REO Sub.

          (f)  Section 4.18 is hereby amended in its entirety to read as
follows:

               4.18 Affiliate Transactions.  The Company and NCFC will not enter
                    ----------------------
               into any transaction with an Affiliate of the Company or NCFC,
               other than transactions in the ordinary course of business on
               terms no less favorable to the Company or NCFC than those that
               would be obtained in an arm's-length transaction, the loans
               described in Section 4.08(e) and transfers of REO to REO Sub as
               described in Section 4.12(c).
 
     3.  Conditions to Effectiveness of this Amendment.  This Amendment shall
         ---------------------------------------------                       
become effective when the Agent shall have received at least thirteen (13)
counterparts of this Amendment, duly executed by the Company and each Lender and
acknowledged by NCFC, provided the following conditions are satisfied:

         (a) Before and after giving effect to this Amendment, the
     representations and warranties of the Company in Section 3 of the Credit
     Agreement, Section 5 of the Pledge and Security Agreement and Section 4 of
     the Servicing Security Agreement, and of NCFC in Section 15 of the
     Guaranty, shall be true and correct as though made on the date hereof,
     except for changes that are permitted by the terms of the Credit Agreement.

         (b) Before and after giving effect to this Amendment, no Event of
     Default and no Unmatured Event of Default shall have occurred and be
     continuing.

         (c) No material adverse change in the business, assets, financial
     condition or prospects of the Company or NCFC shall have occurred since the
     Effective Date.

         (d) The following, each duly executed or certified, as the case may
     be, and dated as of the date of delivery thereof:

              (i)   certified copies of resolutions of the Board of Directors of
         the Company authorizing or ratifying the execution, delivery and
         performance of this Amendment;

              (ii)  a certified copy of any amendment or restatement of the
         Articles of Incorporation or the By-laws of the Company made or entered
         following the date of the most recent certified copies thereof
         furnished to the Lenders;
<PAGE>
 
               (iii)  certified copies of all documents evidencing any necessary
          corporate action, consent or governmental or regulatory approval (if
          any) with respect to this Amendment; and

               (iv)   such other documents, instruments, opinions and approvals
          as the Agent may reasonably request.

     4.   Acknowledgments.  The Company and each Lender acknowledge that, as
          ---------------                                                   
amended hereby, the Credit Agreement remains in full force and effect with
respect to the Company and the Lenders, and that each reference to the Credit
Agreement in the Loan Documents shall refer to the Credit Agreement as amended
hereby.  The Company confirms and acknowledges that it will continue to comply
with the covenants set out in the Credit Agreement and the other Loan Documents,
as amended hereby, and that its representations and warranties set out in the
Credit Agreement and the other Loan Documents, as amended hereby, are true and
correct as of the date of this Amendment.  The Company further represents and
warrants that (i) the execution, delivery and performance of this Amendment is
within its corporate powers and has been duly authorized by all necessary
corporate action; (ii) this Amendment has been duly executed and delivered by
the Company and constitutes the legal, valid and binding obligation of the
Company enforceable against the Company in accordance with its terms (subject to
limitations as to enforceability which might result from bankruptcy, insolvency,
or other similar laws affecting creditors' rights generally and general
principles of equity) and (iii) no Events of Default or Unmatured Events of
Default exist.

     5.   General.
          ------- 

          (a) The Company agrees to reimburse the Agent upon demand for all
     reasonable expenses (including reasonable attorneys fees and legal
     expenses) incurred by the Agent in the preparation, negotiation and
     execution of this Amendment and any other document required to be furnished
     herewith, and to pay and save the Lenders harmless from all liability for
     any stamp or other taxes which may be payable with respect to the execution
     or delivery of this Amendment, which obligations of the Company shall
     survive any termination of the Credit Agreement.

          (b) This Amendment may be executed in as many counterparts as may be
     deemed necessary or convenient, and by the different parties hereto on
     separate counterparts, each of which, when so executed, shall be deemed an
     original but all such counterparts shall constitute but one and the same
     instrument.

          (c) Any provision of this Amendment which is prohibited or
     unenforceable in any jurisdiction shall, as to such jurisdiction, be
     ineffective to the extent of such prohibition or unenforceability without
     invalidating the 
<PAGE>
 
     remaining portions hereof or affecting the validity or enforceability of
     such provisions in any other jurisdiction.

          (d)  This Amendment shall be governed by, and construed in accordance
     with, the internal law, and not the law of conflicts, of the State of
     Minnesota, but giving effect to federal laws applicable to national banks.

          (e)  This Amendment shall be binding upon the Company, the Lenders,
     the Agent and their respective successors and assigns, and shall inure to
     the benefit of the Company, the Lenders, the Agent and the successors and
     assigns of the Lenders and the Agent.
<PAGE>
 
         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
     executed as of the day and year first above written.


                       NEW CENTURY MORTGAGE
                       CORPORATION


                       By:  /s/ Brad Morrice
                            ----------------------------------
                            Its: CEO
                                 -----------------------------

 
                       U.S. BANK NATIONAL ASSOCIATION
 

                       By:  /s/ Edwin Jenkins
                            ----------------------------------
                            Its: Vice President
                                 -----------------------------


                       GUARANTY FEDERAL BANK, FSB


                       By: /s/ W. James Meintjas
                           -------------------------------------
                           Its: Vice President
                                --------------------------------

 

                       COMERICA BANK


                       By: /s/ David R. Chirchill
                           -------------------------------------
                           Its: Assistant Vice President
                                --------------------------------



                    [Signature Page for Second Amendment to
                  Third Amended and Restated Credit Agreement]
<PAGE>
 
                       FIRST UNION NATIONAL BANK,
 

                       By: /s/ C. Simms
                           --------------------------------------
                       Its: Vice President
                            -------------------------------------


                       RESIDENTIAL FUNDING CORPORATION


                       By: /s/ Wendy Joseph
                           --------------------------------------
                       Its: Director
                            -------------------------------------


                       BANK ONE, TEXAS, N.A.


                       By: /s/ Mark L. Freeman
                           --------------------------------------
                       Its: Vice President
                            -------------------------------------

 
                       THE BANK OF NEW YORK


                       By: /s/ Robert w. Pierson
                           ---------------------------------------
                       Its: Vice President
                            --------------------------------------
 



                    [Signature Page for Second Amendment to
                  Third Amended and Restated Credit Agreement]
<PAGE>
 
                       THE FIRST NATIONAL BANK OF
                       CHICAGO


                       By: /s/ Scott Miller
                           -------------------------------------
                       Its: Assistant Vice President
                            ------------------------------------



                       NATIONSBANK OF TEXAS, N.A.


                       By: /s/ Bob Caston
                           -------------------------------------
                       Its: Senior Vice President
                            ------------------------------------



                       FLEET BANK, N.A.


                       By: /s/ ^^ILLEGIBLE SIGNATURE^^
                           -------------------------------------
                       Its: Vice President
                            ------------------------------------



                    [Signature Page for Second Amendment to
                  Third Amended and Restated Credit Agreement]
<PAGE>
 
          THE UNDERSIGNED, NEW CENTURY FINANCIAL CORPORATION, HEREBY (1) AGREES
THAT EACH REFERENCE TO THE CREDIT AGREEMENT, OR WORDS OF SIMILAR IMPORT,
CONTAINED IN THE THIRD AMENDED AND RESTATED GUARANTY DATED AS OF MAY 29, 1998
(THE "GUARANTY") BY THE UNDERSIGNED TO THE LENDERS AND THE AGENT, SHALL BE A
REFERENCE TO THE CREDIT AGREEMENT AS AMENDED BY THE FOREGOING AMENDMENT, (2)
CONFIRMS THAT THE GUARANTY SHALL REMAIN IN FULL FORCE AND EFFECT AFTER GIVING
EFFECT TO THE FOREGOING AMENDMENT, AND (3) CONFIRMS AND ACKNOWLEDGES THAT ITS
REPRESENTATIONS AND WARRANTIES SET FORTH IN SECTION 15 OF THE GUARANTY ARE TRUE
AND CORRECT AS OF THE DATE OF THE FOREGOING AMENDMENT.

                       NEW CENTURY FINANCIAL CORPORATION

                       By: /s/ Brad Morrice
                           ---------------------------------------
                       Its: President
                            --------------------------------------