Mid-infrared lasers hold significant application demands in fields such as medicine, communications, and national defense. In recent years, research on mid-infrared fiber lasers has attracted extensive attention worldwide. This work demonstrates a high-power mid-infrared light source at 4.16 μm utilizing HBr gas-filled anti-resonant hollow-core fiber (AR-HCF). By employing a homemade 2 μm single-frequency fiber amplifier as the pump source and utilizing the intrinsic absorption of gas molecules to achieve population inversion, we have realized over 10 W continuous wave mid-infrared output through backward gas-filling method in large-mode-area (AR-HCF). This optimized configuration simultaneously enhances the optical-to-optical conversion efficiency and effectively suppresses thermal accumulation limitations. At the maximum incident pump power of 63.8 W, the system achieves a maximum continuous output power of 10.37 W with corresponding slope efficiency of approximately 16.8%. The beam quality measurement reveals M²<1.1 at maximum power operation. This research verifies the substantial capability of fiber gas lasers to generate high-power mid-infrared radiation, providing valuable insights for advancing the development and investigation of mid-infrared fiber laser technologies.