Bispecific chimeric antigen receptor T-cell (CAR-T) therapies have shown promising results in clinical trials for advanced B-cell malignancies. However, it is challenging to broaden the success of bispecific CAR-T therapies to treat refractory/relapse (r/r) T-cell leukemia/lymphoma because targeting multiple T-cell-expressing antigens leads to exacerbated CAR-T cell fratricide and potential safety concerns. Fully human heavy chain variable (FHVH) antibodies that specifically target CD5 or CD7 were screened and constructed to CD5/CD7 bispecific CARs. A truncated Epidermal growth factor receptor were integrated into CAR constructs to address safety concerns. To tackle the fratricidal issue of CAR-T cells targeting T-cell-pan marker(s), CRISPR/Cas9-based CD5 and CD7 genes knockout were performed before lentiviral transduction of bispecific CARs. Functional comparison between different bispecific CAR structures: tandem CARs and dual CAR were performed in vitro and in vivo to determine the optimal construct suitable for addressing T-cell malignancy antigen escape in clinical setting. Knockout of CD5 and CD7 prevents fratricide of CD5/CD7 bispecific CAR-T cells, and FHVH-derived CD5/CD7 bispecific CAR-T cells demonstrate potent antitumor activity in vitro and in vivo. The fratricide-resistant FHVH-derived CD5/CD7 bispecific CAR-T cells have potent antitumor activity against T-cell malignancies, and tandem CARs are more effective than dual CAR in preventing tumor escape in heterogeneous leukemic cells. The meaningful clinical efficacy and safety of tandem CD5/CD7 CAR-T cells deserve to be explored urgently.