A new copolymer poly (aryl ether ketone) (PAEK) resin was used as a matrix to prepare carbon fiber (CF) reinforced composites with different crystallinity by slow and rapid cooling. Finite element (FE) models were constructed according to micromechanics, and the progressive damage method based on the three-dimensional (3D) PUCK damage criterion was used to analyze the low-velocity impact damage mechanism of the CF/PAEK composites. The experimental results show that the composites with lower crystallinity have higher impact resistance and smaller impact damage area. In the FE simulated impact damage evolution process, the damage of the impact side is mainly compressive damage of the matrix and the fiber, while that of the impact back side is mainly tensile damage of the matrix. Moreover, due to their high interfacial bonding strength, the main damage modes of rapid-cooled composites with lower crystallinity are severe matrix tensile damage and slight fiber tensile damage in the impact back side. However, the slow-cooled composites show more delamination. In addition, for the damage evolution of compression after impact, the FE simulation shows that fiber compression, matrix tension, matrix compression and delamination expand along the transverse to the compression load. Furthermore, the in-plane damage expansion occurs earlier in the rapid-cooled composites, which also have graver interlaminar damage.