In response to the challenges of complex terrain, widely distributed task points, and low efficiency in task allocation and path planning for Unmanned Aerial Vehicle (UAV) power inspection tasks in large mountainous areas, a hybrid optimization algorithm based on the black-winged kite and Arctic puffin optimizer (HBAO) is proposed, which can coordinate task allocation and path planning of UAV. First, an optimization objective function is established based on constraints such as total flight distance, average flight altitude, and terrain threats. Next, an improved distance-weighted random step size search strategy is employed to enhance the predation phase of the Black-winged Kite Algorithm, strengthening the algorithm’s global search capability. Then, a Fitness and Distance-Based (FDB) strategy for optimal individual selection is introduced to improve the global search efficiency and optimization accuracy of the Black-winged Kite Algorithm during the migration phase. Finally, the cooperative hunting mechanism of the Arctic Puffin Algorithm is incorporated, allowing for individual collaboration in updating positions, which can effectively enhance the algorithm’s ability to escape from local optima and ensures diversity and efficiency in global search. Simulations conducted using a Digital Elevation Model (DEM) of the Qinling Mountains demonstrate that, in scenarios with numerous inspection task points, the overall performance of the proposed HBAO outperforms that of six comparison algorithms, significantly reducing global costs.