The experimental progress of laser equation of state (EOS) studies at Shanghai Institute of Laser Plasma (SILP) is discussed in this paper. With a unique focal system, the uniformity of the laser illumination on the target surface is improved and a laser-driven shock wave with good spatial planarity is obtained. With an inclined aluminum target plane, the stability of shock waves are studied, and the corresponding thickness range of the target of laser-driven shock waves propagating steadily are given. The shock adiabats of Cu, Fe, SiO2 are experimentally measured. The pressure in the material is heightened remarkably with the flyer increasing pressure, and the effect of the increasing pressure is observed. Also, the high-pressure shock wave is produced and recorded in the experimentation of indirect laser-driven shock waves with the hohlraum target.