Inclusion Criteria:  Patients and legally acceptable representative must have voluntarily signed Informed Consent Form and willing to complete the study procedure, after fully understanding of the study. Age ≥ 18 years and ≤ 70 years, male or female. The patients have received at least 3 prior regimen for multiple myeloma. Subjects should have received treatment with at least one proteasome inhibitor and one immunomodulatory drug (IMiD; and have been stable disease, relapsed or progressed after treatment with at least one regimen consisting of above-mentioned medications. Subjects should have relapsed within 12 months after the last line of therapy, or not achieved at least minimal response (MR) or disease has progressed within 60 days after last line of therapy (IMWG criteria 2016), with documented evidence. Subjects should have measurable disease per IMWG 2016 criteria. Expected survival > 12 weeks. Eastern Cooperative Oncology Group (ECOG) scores 0 - 1. Subjects should have adequate hemostatic and liver and kidney meet the following examination criteria: (without ongoing supportive treatments):  1) Complete blood count (CBC) results: absolute neutrophil count（ANC） ≥ 1.0 × 109/L, platelet count ≥ 75 × 109/L (if the proportion of plasma cells in the bone marrow is > 50%, subjects with platelets ≥ 50 × 109/L will be eligible), Hb ≥ 70 g/L.  2) Blood biochemistry: creatinine clearance ≥ 40 mL/min (Cockcroft-Gault formula), alanine aminotransferase (ALT) ≤ 2.5 × upper limit normal (ULN)，aspartate aminotransferase (AST) ≤ 2.5 × ULN, total bilirubin ≤ 2 × ULN.  10. Women of childbearing age must undergo a serum pregnancy test with negative results at screening and before lymphodepletion and be willing to use an effective and reliable method of contraception for at least 1 year after T cell infusion. All female subjects are prohibited from egg donation within 1 year after T cell infusion.  11. Men must be willing to use an effective and reliable method of contraception for at least 1 year after T cell infusion if they have sexual activity with women of childbearing potential. All male subjects are prohibited from sperm donation within 1 year after T cell infusion.  Exclusion Criteria:  Pregnant or lactating women. Subjects positive for any following tests: human immunodeficiency virus (HIV) antibody, Treponema pallidum (syphilis) antibody, hepatitis C virus (HCV) antibody, hepatitis B virus (HBV) surface antigen (HBsAg) and HBV DNA. Subjcets with any uncontrolled active infection, including but not limited to active tuberculosis (TB) (judged by investigator). Subjects with AEs from previous treatment that have not recovered to Common Terminology Criteria for Adverse Events (CTCAE) v5.0 ≤ 1, excluding hair loss and other events that the treating physician considers as tolerable. Subjects who have received CAR T therapy for any targets. Subjects who have had anti-B Cell Maturation Antigen（BCMA） therapy. Subjects who have received allogeneic stem cell transplantation for multiple myeloma. Subjects who have received autologous stem cell transplantation less than 12 weeks before leukapheresis. Subjects who have received any anti-myeloma treatment 14 days before leukapheresis, including but not limited to cytotoxic therapy, proteasome inhibitor, immunomodulator, target therapy, monoclonal antibodies, radiotherapy, epigenetic therapy or investigational drug, or the use of invasive investigational medical device. If the field of radiation covers ≤ 5% of the bone marrow, the subjects are eligible to participate in the study regardless of the radiotherapy end date. Subjects who have received ≥ 15 mg prednisone daily or other equivalent dose of steroids within 7 days before leukapheresis, except inhaled steroids. Subjects who have plasma cell leukemia, Waldenström macroglobulinemia, POEMS syndrome or primary light chain amyloidosis. Subjects who have been received a live attenuated vaccine 4 weeks before leukapheresis. Subjects allergic to or intolerant of fludarabine, cyclophosphamide, tocilizumab, or allergic to the ingredients (DMSO) of CT0590 T cell preparations; subject with confirmed another serious allergy history. Subjects who have any of the following conditions within 6 months prior to the signing of inform consent: uncontrolled congestive heart failure (New York Heart Association (NYHA) stage III or IV), angina, myocardial infarction, stroke (except lacunar infarct), coronary artery bypass graft, clinically meaningful (judged by investigator) arrhythmia (including but not limited to ventricular arrhythmia, significant QT interval prolongation (Bazett's formula corrected QT,corrected QT ≥ 500 ms, judged by investigator), uncontrolled blood pressure as defined as systolic > 160 mmHg, diastolic >100 mmHg, uncontrolled diabetes as defined as HbA1c >8% after treatment, pulmonary embolism, or other conditions that the investigator believe that participating in this clinical trial may endanger the health of the subjects. Blood oxygen saturation that can only be maintained at > 95% by oxygen inhalation before leukapheresis. Subjects known to have active autoimmune diseases including but not limited to psoriasis, rheumatoid arthritis and other conditions that require long-term immunosuppressive therapy. Subjects with second malignancies in addition to multiple myeloma are not eligible if the second malignancy has required treatment within the past 5 years, with the exception of low grade malignancies. Subjects who have central nervous system (CNS) metastases or symptomatic CNS involvement. Subjects who are unable or unwilling to comply with the requirements of clinical trial or other reasons that are not suitable for participating in the clinical trial. Subjects who have received major surgery 2 weeks prior to leukapheresis or plan to receive major surgery within 4 weeks after cell infusion (excluding cataract and other local anesthesia). Subjects who are related to investigator or study personnel, or with possible conflict of interest with the investigator or study personnel.