Exhibit 31.1

Rule
13a-14(a)/15d-14(a) Certifications

I,
Thomas C. McGraw, certify that:

| | 1. | I
                                         have reviewed this annual report on Form 10-K of FNB Bancorp;
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| | 2. | Based
                                         on my knowledge, this annual report does not contain any untrue statement of a material
                                         fact or omit to state a material fact necessary to make the statements made, in light
                                         of the circumstances under which such statements were made, not misleading with respect
                                         to the period covered by this report;
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| | 3. | Based
                                         on my knowledge, the financial statements, and other financial information included in
                                         this report, fairly present in all material respects the financial condition, results
                                         of operations and cash flows of the registrant as of, and for, the periods presented
                                         in this report;
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| | 4. | The
                                         registrant’s other certifying officer and I are responsible for establishing and
                                         maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e)
                                         and 15d-15(e)) and internal control over financial reporting (as defined in Exchange
                                         Act Rules 13a-15(f) and 15d-15(f) for the registrant and have:
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| | a) | Designed
                                         such disclosure controls and procedures, or caused such disclosure controls and procedures
                                         to be designed under our supervision, to ensure that material information relating to
                                         the registrant, including its consolidated subsidiaries, is made known to us by others
                                         within those entities, particularly during the period in which this annual report is
                                         being prepared;
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| | b) | Designed
                                         such internal control over financial reporting, or caused such internal control over
                                         financial reporting to be designed under our supervision, to provide reasonable assurance
                                         regarding the reliability of financial reporting and the preparation of financial statements
                                         for external purposes in accordance with generally accepted accounting principles;
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| | c) | Evaluated
                                         the effectiveness of the registrant’s disclosure controls and procedures and presented
                                         in this report our conclusions about the effectiveness of the disclosure controls and
                                         procedures, as of the end of the period covered by this report based on such evaluation;
                                         and
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| | d) | Disclosed
                                         in this report any change in the registrant’s internal control over financial reporting
                                         that occurred during the registrant’s fourth fiscal quarter that has materially
                                         affected, or is reasonably likely to materially affect, the registrant’s internal
                                         control over financial reporting; and
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| | 5. | The
                                         registrant’s other certifying officer and I have disclosed, based on our most recent
                                         evaluation of internal control over financial reporting, to the registrant’s auditors
                                         and the audit committee of registrant’s board of directors:
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| | a) | All
                                         significant deficiencies and material weaknesses in the design or operation of internal
                                         control over financial reporting which are reasonably likely to adversely affect the
                                         registrant’s ability to record, process, summarize and report financial information;
                                         and
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| | b) | Any
                                         fraud, whether or not material, that involves management or other employees who have
                                         a significant role in the registrant’s internal control over financial reporting.
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| |    |                                                                                                                                                                                                                                                             

|Date: May 12, 2017 |                        
|------------------ | -----------------------
|                   | /s/ Thomas C. McGraw   
|                   | Thomas C. McGraw       
|                   | Chief Executive Officer

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