Abstract: The equation of state and the Hugoniot shock relationship of granite at high pressure were studied by experiments of high- and hyper-velocity flyer impact using a two-stage light gas gun. The average shock wave velocity in the experimental sample was measured by a fiber optic probe. The maximum impact velocity was 4.47 km/s, and the corresponding maximum impact pressure was 42.4 GPa. By fitting the effective experimental results, the Hugoniot linear relationship, Hugoniot parameters C and λ, and polynomial equations of the granite at high pressure were obtained. The results provided a reference for the application of granite in rock blasting, meteorite impact and other fields.