ZnO films with c-axis (0002) orientation have been successfully grown by RF magnetron sputtering on Al2O3/glass substrates. The alumina films were firstly deposited on glass substrates, and then secondly deposited on interdigital transducer/ZnO film/alumina film/glass substrates by electron beam evaporation. The crystalline structure and surface roughness of the films were investigated by X-ray diffraction and atomic force microscopy, respectively. The phase velocity and coupling coefficient of the surface acoustic wave (SAW) device were both increased when we deposited the double alumina layers. On the other hand, the temperature coefficient of frequency becomes better if we increase the thickness of the lower alumina film. The experimental result is beneficial for improving the performance of the ZnO thin-film SAW devices on inexpensive glass substrates.