Inclusion Criteria:  The patient volunteered to participate in the study and signed the Informed Consent; Age, 18-70 years (include 18 and 70), male or female; Expected survival ≥ 12 weeks Eastern Cooperative Oncology Group score 0-2 CD19 or CD20 positive B-Non-Hodgkin's lymphoma confirmed by cytology or histology according to World Health Organization 2016 criteria;  Patients with a clear diagnosis of relapsed and/or refractory B-Non-Hodgkin's lymphoma, including Diffuse Large B Cell Lymphoma, Follicular Lymphoma and Mantle Cell Lymphoma. Diffuse Large B Cell Lymphoma includes the following types:  Diffuse Large B Cell Lymphoma, Non Specifically Primary Mediastinal B-cell Lymphoma Transformed Follicular Lymphoma High Grade B-Cell Lymphoma With MYC and BCL2 and/or BCL6 High Grade B-Cell Lymphoma, Non Specifically 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; No contraindications of apheresis. At least one measurable lesion according to Lugano 2014 criteria;  Adequate organ function and adequate bone marrow reserve  Hemoglobin≥80 g/L Absolute neutrophil count≥1.0×109/L Platelet≥50×109/L, Creatinine≤1.5×upper limit of the normal range (ULN) Cardiac ejection fraction≥50% Saturation of Pulse Oxygen>92% Total bilirubin≤1.5×ULN Alanine Aminotransferase/Aspartate Aminotransferase≤3×ULN  Exclusion Criteria:  Malignant tumors other than B-Non-Hodgkin's lymphoma within 5 years prior to screening, except cervical carcinoma in situ, basal cell or squamous cell skin cancer, local prostate cancer after radical surgery, and breast ductal carcinoma in situ after radical surgery; Human Immunodeficiency Virus, Hepatitis B Virus, Hepatitis C Virus or treponema pallidum infection ; Any instability of systemic disease, including but not limited to active infection (except local infection), severe cardiac, liver, kidney, or metabolic disease need treatment; 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 their cell transfusion; Active or uncontrolled infections requiring systemic treatment within 14 days before enrollment; Patients who have been previously infected with tuberculosis; Administered Corticosteroids and/or other immunosuppressants within 7 days before apheresis. and 5 days before the infusion of C-CAR039; Patients with central nervous system involvement;