This study is conducted on glass fiber-reinforced composite honeycomb sandwich structures by introducing delamination damage through low-velocity impact tests, establishing a three-dimensional progressive damage analysis model, and evaluating the delamination damage characteristics and laws of honeycomb sandwich structures under different impact energies through experiments. Repair techniques and process parameters for delamination damage are explored. It is found that as the impact energy increases, the damage area of honeycomb sandwich panels also increases, and the delamination damage extends from the impact center to the surrounding areas, accompanied by damage such as fiber fracture and matrix cracking. The strength recovery rates of sandwich panels at impact energies of 5 J, 15 J, and 25 J after repair are 71.90%, 65.89%, and 67.10%, respectively, which has a considerable repair effect. In addition, a progressive damage model for low-velocity impact on the composite honeycomb sandwich structure is established, and its accuracy and reliability are verified.