This is a single-center, open-label study to evaluate the safety and efficacy of C-CAR039 in relapsed and/or refractory B-NHL patients.

The study will include the following sequential phases: Screening, Apheresis and C-CAR039 manufacturing, Baseline testing, Lymphodepleting, C-CAR039 infusion, and Follow-up Visit.

Criteria: Inclusion Criteria:

1. Age 18-70 years (include 18 and 70), male or female;
2. Expected survival ≥ 12 weeks
3. ECOG score 0-2
4. CD19 or CD20 positive B-NHL confirmed by cytology or histology according to WHO2016 criteria, including DLBCL, PMBCL, tFL, FL and MCL
5. Relapsed or refractory disease after ≥ 2 lines (for FL, at least 3 lines) of standard therapy or relapsed after autologous stem cell transplantation (ASCT);
6. For CD20-positive subjects, they should have received at least one regimen containing anti-CD20-targeted therapy (such as rituximab). If they do not complete the regimen due to intolerance, the cause of intolerance should be recorded;
7. No contraindications of apheresis.
8. At least one measurable lesion according to Lugano 2014 criteria;
9. Adequate organ and bone marrow function
10. The patient volunteered to participate in the study and signed the Informed Consent.

Exclusion Criteria:

1. Malignant tumors other than diffuse large B-cell lymphoma, follicular lymphoma and mantle cell lymphoma within 5 years before screening, except fully treated cervical carcinoma in situ, basal cell or squamous cell skin cancer, local prostate cancer after radical operation and breast ductal carcinoma in situ after radical operation;
2. Active HIV, HBV, HCV or treponema pallidum infection;
3. Any instability of systemic disease, including but not limited to active infection (except local infection), severe cardiac, liver, kidney, or metabolic disease need therapy
4. Any other uncontrolled active disease that hinders participation in the trial;
5. Any situation that the investigator believes would compromise the safety of the subject or interfere with the purpose of the study;
6. Female subjects who have been pregnant or breastfeeding, or who plan to conceive during or within 1 year after treatment, or male subjects' partner plans to conceive within 1 year after C-CAR039 infusion;
7. Active or uncontrolled infections requiring systemic treatment within 14 days before enrollment;
8. Patients who have previously been infected with tuberculosis.
9. Administered Corticosteroids and/or other immunosuppressants within 7 days before apheresis. and 5 days before the infusion of C-CAR039;
10. Patients with central nervous system involvement;
11. Any systemic antitumor therapy performed within 2 weeks before enrollment;
12. Those with medical conditions that prevent them from signing the written informed consent or from complying with the study procedures; or those who are unwilling or unable to comply with the study requirements;
13. Other conditions was considered unsuitable for enrollment by the investigator.