A preparation of autologous T-lymphocytes that have been genetically modified and transduced with a lentiviral vector expressing a T-cell-receptor (TCR) complex-based chimeric antigen receptor (CAR) specific for two different epitopes of the immune inhibitory receptor leukocyte immunoglobulin-like receptor B member 4 (LILRB4; ILT3; ILT-3), with potential immune checkpoint inhibitory and antineoplastic activities. Upon administration, autologous anti-LILRB4 CAR-T cells target and bind to two different epitopes of LILRB4 expressed on tumor cells. This results in a cytotoxic T-lymphocyte (CTL) response against LILRB4-expressing tumor cells. LILRB4, a tumor associated antigen (TAA) and an immune inhibitory receptor expressed on immune suppressive myeloid cells, is highly expressed on certain hematologic cancer cells, such as monocytic acute myeloid leukemia (AML) cells. It functions as an immune checkpoint that negatively regulates T-cell activation as its extracellular domain inhibits T-cell activity. It plays an important role in tumor infiltration, T-cell suppression and immune tolerance.