We identify amino acid variants within dominant SARS-CoV-2 T-cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T-cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T-cell responsiveness was seen due to Q213K in the A*01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215, due to P13L, P13S and P13T in the B*27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17, and due to T362I and P365S in the A*03:01/A*11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T-cell lines unable to recognise variant epitopes have diverse T-cell receptor repertoires. These data demonstrate the potential for T-cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T-cell as well as humoral immunity.