Chimeric antigen receptor (CAR) T cell therapy is an effective method for treating specific cancers. CARs are normally designed to recognize antigens, which are highly expressed on malignant cells but not on T cells. However, when T cells are engineered with CARs that recognize antigens expressed on the T cell surface, CAR T cells exhibit effector function on other T cells, which results in fratricide, or killing of neighboring T cells. Here, using human leukocyte antigen-DR (HLA-DR)-targeted CAR T cells, we show that weak affinity between CAR and HLA-DR reduces fratricide and induces sustained CAR downregulation, which consequently tunes the avidity of CAR T cells, leading to desensitization. We further demonstrate that desensitized CAR T cells selectively kill Epstein-Barr virus-transformed B cells with enhanced HLA-DR expression, while sparing normal B cells. Our study supports an avidity-tuning strategy that permits sensing of antigen levels by CAR T cells.