Ge-As-Se chalcogenide glasses were prepared and the surface damage characteristics under femtosecond laser irradiation were experimentally investigated. Femtosecond laser beams with different power intensities, focusing depths, pulse repetition rates, and pulse numbers were employed to determine the damage thresholds of the samples. The surface morphologies and feature sizes of the damage craters were studied with regard to laser energy density to evaluate the damage circumstances of the glasses. The generation of the surface damage was also recorded by using different numbers of pulses. Results showed that the damage area increased monotonically with the laser power at low energy density and tended to saturation when reaching a critical value. According to the linear circumstances of laser energy density on the damage crater area, the average damage thresholds of the Ge-As-Se glasses with different repetition rates and pulse numbers were obtained. Results showed that the damage threshold decreased with the increase in pulse repetition rate and number of pulse.