Laser shock peening (LSP) is an innovative and promising surface strengthening technique of metallic materials. The LSP-induced plastic deformation, the compressive residual stresses and the microstructure evolution are essentially attributed to the laser plasma-induced shock wave. A three-dimensional finite element model in conjunction with the dislocation density-based constitutive model was developed to simulate the LSP of pure Al correlating with the LSP-induced shock wave, and the predicted in-depth residual stresses are in reasonable agreement with the experiment results. The LSP-induced shock wave associated with the laser spot diameter of 8.0 mm propagates in the form of the plane wave, and attenuates exponentially. At the same time, the propagation and attenuation of the LSP-induced shock wave associated with the laser spot diameter of 0.8 mm are in the form of the spherical wave. The reflection of the LSP-induced shock wave at the bottom surface of the target model increases the plastic deformation of the target bottom, resulting in the increase of dislocation density and the decrease of dislocation cell size accordingly. Reducing the target thickness can significantly increase the reflection times of the LSP-induced shock wave at the bottom and top surfaces of the target model, which is considered to be conductive to the generation of the compressive residual stress field and grain refinement.