Ge-As-Se-Te (GAST) chalcogenide glass has ultra-wide transmission range of more than 20 μm, an excellent optical material that can be applied in mid-infrared (MIR) and far-infrared (FIR). In this work, the Ge_xAs_40-xSe₄₀Te₂₀ (x=0, 10, 20, 30, 40 mol%) chalcogenide glasses were prepared by the fusion quenching method, and the optical properties were tested. The sample glass was irradiated with femtosecond lasers of different wavelengths (800 nm, 3 μm and 4 μm), different powers and repetition frequencies, and the laser damage characteristics of GAST were studied by scanning electron microscopy (SEM) and Raman spectroscopy. With the increase of Ge content, the laser-induced damage threshold (LIDT) at 800 nm reaches a maximum of 40.16 mJ/cm² at Ge₃₀As₁₀Se₄₀Te₂₀. The LIDT increase with wavelength of the femtosecond laser and reaches 81.09 mJ/cm² at 4 μm. In addition, the results show that LIDT will gradually decrease as the number of laser pulses and the repetition rate increase.