In order to improve the flight efficiency of a flying–walking power transmission line inspection robot (FPTLIR) during flight missions, an accurate energy consumption model is constructed, and a multiobjective optimization approach using the improved NSGA-II is proposed to address the high energy consumption and long execution time. The energy consumption model is derived from the FPTLIR kinematics to the motor dynamics, with the key parameters validated using a test platform. A multiobjective optimization model is proposed that considers many constraints related to the FPTLIR during missions, offering a comprehensive analysis of the energy consumption and execution time. The NSGA-II algorithm is improved by integrating the Cauchy variation operator and the simulated annealing algorithm, which is used to construct the multiobjective optimization approach. Simulation and experimental results demonstrate that the proposed model accurately predicts the energy consumption of the FPTLIR across different paths and flight conditions with an average relative error ranging from 0.76% to 3.24%. After optimization, energy savings of 5.33% and 5.01% are achieved for on-line and off-line missions, respectively, while maintaining the shortest execution time at the given energy level. The energy consumption optimization approach significantly improves the flight efficiency of the system, providing a reference for analyzing and optimizing energy consumption of inspection robots.