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The damage of high-voltage terminal shed of composite insulators can influence the flashover performance of the insulators. The study was carried out experimentally to investigate the flashover characteristics of composite insulators with sheds damage at different voltage levels. The results show that sheds damage would decrease pollution flashover voltage, creepage distance flashover voltage gradient E_L and the dry arc distance flashover voltage gradient E_H, and such decrease range was proportional to damage degree. Besides, with the increase of composite insulator's dry arc distance, effects of sheds damage on pollution flashover voltage, creepage distance flashover voltage gradient E_L and the dry arc distance flashover voltage gradient E_H were gradually decreasing. With the ESDD ranging from 0.1 mg/cm to 0.3 mg/cm², AC pollution flashover voltage of 35 kV, 110 kV and 220 kV composite insulators decreased by up to 35.92%, 15.03%, 9.11% respectively; the creepage distance flashover voltage gradient E_L decreased by up to 19.15%, 6.05%, 1.34% respectively; the dry arc distance flashover voltage gradient E_H decreased by up to 35.92%, 15.03%,9.11% respectively.