CAR-T cells for cancer therapy are provided with an antibody that recognizes the MAGE-A4-derived-peptide/HLA-A2 complex. The antibody includes the VH amino acid sequence of SEQ ID NO: 36 and the VL amino acid sequence of SEQ ID NO: 38. The antibody preferably is provided with the amino acid sequence of SEQ ID NO: 32. Such CAR-T cells can be used in CAR infusion therapy in which a cancer-specific intracellular antigen is used.