The propagation characteristics of surface acoustic wave for the ZnO piezoelectric films and nanocrystalline diamond (NCD) films multilayer SAW devices on Si substrates were investigated. High surface acoustic wave velocity is achieved for a ZnO/NCD/Si multilayer structure excited by a bottom-electroded device configuration. The NCD films deposited on Si substrates (NCD/Si) not only possess smooth surface, but also show good compatibility with ZnO materials, such that  textured ZnO films can be directly grown on NCD/Si substrates without the necessity of using buffer layer. The surface acoustic wave velocity increased with the thickness of the NCD films. For the thickness of the ZnO and NCD films investigated, the 0th mode surface acoustic velocity in IDT/ZnO/NCD/Si structure achieves 5100 m/s, whereas the 1st mode SAW in the ZnO/IDT/NCD/Si structure reaches 8500 m/s.