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Considering the trajectory planning problem of rotor unmanned aerial vehicle (UAV) for inspection of cable-stayed bridge tower, a trajectory planning method of rotor UAV for cable-stayed bridge inspection is proposed. In this method, the energy consumption of the rotor UAV during patrol inspection is taken as the evaluation index of the trajectory quality. The improved genetic algorithm based on information entropy theory is used to obtain the trajectory, which possesses the least energy consumption. The double arc obstacle avoidance strategy is proposed to re-plan the trajectory in the local area, where the stayed-cable obstacle exists. Thus, the stayed-cable obstacle can be avoided effectively and ensure flight safety of rotor UAV. The simulation results of the inspection of the cable towers of Weicheng Bridge in Xianyang show that the proposed method can effectively reduce the energy consumption of the patrol rotor UAV, ensure the flight safety of the patrol rotor UAV, and can be well applied to the external inspection of cable-stayed bridge tower.