The application of As-Se chalcogenide glasses in high-power laser delivery is hindered by their low damage threshold due to their weak chemical bonds. To solve this, we introduced germanium elements into the As-Se glasses and optimized the composition to raise the glass transition temperature (Tg) and enhance the laser damage threshold (LDT). From the correlation among various parameters including Tg, LDT, and fiber loss, we concluded an optimized composition of Ge23As13.5Se63.5/Ge23As12.5Se64.5 glass. After effective purification and preform extrusion, the glasses were processed into high-quality step-index fiber (core diameter of 300 µm), which exhibits a minimum loss of 0.9 dB/m at 6.9 µm and is capable of withstanding an input CO2 laser power of 19.96 W at a wavelength of 10.6 µm, equal to a power density of 28.25 ± 0.02 kW/cm2 in air. This is nearly 2.3 times higher than that previously reported for Ge-As-Se fibers. This establishes a material foundation for achieving far-infrared high-energy laser systems using Ge-As-Se fibers in the future.