Abstract: The microstructure of metals significantly impacts their macroscopic mechanical properties, and a deep understanding of the mechanical response of metals under dynamic conditions is of great significance. Peridynamics, an emerging nonlocal theory, has a natural theoretical advantage in studying the damage and failure of materials under impact. In this paper, the theory of non-ordinary state-based peridynamics is used as the theoretical framework to simulate the propagation of waves in anisotropic materials and the interaction between waves and microstructures. To accurately capture shock waves in the nonlocal model, the interface pressure in the nonlocal force state is corrected using a non-iterative approximate Riemann solution, ensuring the conservation and solution stability of the physical quantities at the shock wave interface, and taking into account computational efficiency. Based on crystal plasticity theory and homogenization theory, the finite deformation crystal viscoplastic constitutive model is introduced into the nonlocal theoretical framework of peridynamics. Comparisons with analytical solutions show that the proposed model can effectively eliminate non-physical oscillations behind the wavefront and accurately capture the elastoplastic wave structure. Comparisons with experimental results show that the macroscopic mechanical response obtained from the efficient explicit crystal viscoplastic peridynamics simulation is in good agreement. On this basis, the effects of different impact velocities and the initial microstructure of the material on the anisotropy of the impact response and the heterogeneity of plastic deformation are discussed. The crystal orientation determines the Hugoniot elastic limit and also the soft and hard orientations of the material, thereby affecting the evolution of the elastoplastic wave structure. Grain boundaries lead to highly heterogeneous stress distributions and cumulative slip strains in the Hugoniot state.