The plate-impact experiment was used to measure the response of shock pressure and the equation of state (EOS) of Zr₄₁Ti₁₄Ni_12.5Cu₁₀Be_22.5 amorphous alloy. The particle velocities of free surface were tested under impact from copper plate with the velocity from 350 m/s to 550 m/s. The Hugoniot parameters of the material were calculated by using impedance matching method, and the experimental results were compared with the computational results calculated by ideal mixture model. The problem to solve the Gruneisen EOS of the material was turned into nonlinear optimization. A novel numerical method based on simulated annealing algorithm was developed to analyze the Gruneisen EOS of the material, and the annealing scheme was designed. The Birch-Murnaghan equation and the Trinomial equation of the material were proposed by analytical method, and compared with Gruneisen EOS and the experimental results. The experimental and theoretical results show that within the pressure between 5 GPa and 10GPa, the zero-pressure volume velocity of Zr₄₁Ti₁₄Ni_12.5Cu₁₀Be_22.5 amorphous alloy was 4267 m/s, the slope of D-u curve was 4.376, which is much larger than normal metal, and the Hugoniot limit of the material was around 5.6 GPa. The ideal mixture model is only applicable to calculate the Hugoniot parameters of Zr-based amorphous alloy in high-pressure phase, whereas considerable errors will be caused under low pressure. The Gruneisen EOS and Trinomial EOS matched the experimental results well within the pressure between 5 GPa and 10 GPa, while there were major errors between the experimental results and the Birch-Murnaghan equation.