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We evaluate the performance of GaAs-GaP core-shell (C-S)-nanowire (NW) field-effect transistors by employing a semiclassical ballistic transport model. The valence-band structures of GaAs-GaP C-S NWs are calculated by using a kldrp method including the strain effect. The calculations show that the strain causes substantial band warping and pushes valence subbands to move up. We demonstrate that the on current can be enhanced with the strength of strain induced in the core, but an extremely thin equivalent oxide thickness may suppress the effect of the strain-induced current improvement. The achieved results can provide a design guide for optimizing device performance.