Vertically aligned ZnO/ZnTe core-shell nanowires were grown on a-plane sapphire substrate by using chemical vapor deposition with gold as catalyst for the growth of ZnO core and then followed by growing ZnTe shell using metal-organic chemical vapor deposition (MOCVD). Transmission electron microscope (TEM) and Raman scattering indicate that the core-shell nanostructures have good crystalline quality. Three-dimensional fluorescence images obtained by using laser scanning confocal microscope demonstrate that the nanowires have good optical properties. The core-shell nanowire was then fabricated into single nanowire field effect transistor by standard e-beam photolithography. Electrical measurements reveals that the p-type ZnO/ZnTe FET device has a turn on voltage of -1.65 V and the hole mobility is 13.3 cm2/V s.