The main failure modes of composite materials during low-velocity impact are matrix failure, interlaminar delamination, and fiber damage, and the impact problem is relatively complex, so it is crucial to choose the type of failure criterion and damage evolution method. In view of this, a progressive failure model is developed for the low-velocity impact problem of composite laminates. The Puck criterion is used to predict the matrix damage during the impact process, the Selective Range Golden Section Search (SRGSS) algorithm is used to search for the fracture surface angle of the matrix, and the strain-based Hashin failure criterion is used to determine the damage initiation of the fibers, while the bilinear constitutive model is used to simulate the damage evolution process. The interlaminar delamination damage is predicted by the cohesive element, using the quadratic stress criterion as the delamination damage initiation criterion and the B-K criterion to determine the delamination damage evolution. The low-velocity impact test and simulation analysis are applied to the composite laminates to obtain the damage size, damage shape, and damage distribution, to obtain the damage propagation law, and to analyze the damage mechanism of low-velocity impact. By comparing the simulation results with the experimental data, the validity of the model was verified.