By introduction of the high order thermal expansion coefficients and the high order thermal elastic constants of material,the equations of surface acoustic wave propagation in a semi infinite quartz crystal have been solved and the wave velocities at different temperature have obtained. Numerical results showed that temperature change has strong effect on wave velocities of surface acoustic wave propagation in AT cut and ST cut quartz crystal.Then we investigated the frequency temperature characteristics of surface acoustic wave propagation in ST cut quartz crystal and found that the frequency shift caused by temperature change is significant.