Identifying T-cell receptors (TCRs) that bind tumor-associated antigens (TAAs) with optimal affinity is a key bottleneck in the development of adoptive T-cell therapy of cancer. TAAs are unmutated self proteins, and T cells bearing high-affinity TCRs specific for such antigens are commonly deleted in the thymus. To identify optimal-affinity TCRs, we generated antigen-negative humanized mice with a diverse human TCR repertoire restricted to the human leukocyte antigen (HLA) A*02:01 (ref. 3). These mice were immunized with human TAAs, for which they are not tolerant, allowing induction of CD8⁺ T cells with optimal-affinity TCRs. We isolate TCRs specific for the cancer/testis (CT) antigen MAGE-A1 (ref. 4) and show that two of them have an anti-tumor effect in vivo. By comparison, human-derived TCRs have lower affinity and do not mediate substantial therapeutic effects. We also identify optimal-affinity TCRs specific for the CT antigen NY-ESO. Our humanized mouse model provides a useful tool for the generation of optimal-affinity TCRs for T-cell therapy.