This paper presents an anti-swing control method to prevent situations where inspection robots detach and fall off transmission lines during obstacle crossing due to excessive swing angles caused by the rotation of the robot around the transmission line. Firstly, an obstacle-crossing model for the inspection robot was constructed and the causes of robot swinging phenomena were analyzed, in addition to their impact on obstacle crossing stability. By combining this with the obstacle-crossing model, a moment balance equation was established for the inspection robot. This equation can be used to solve mapping relationships between body offset and the tilt angle of transmission line gripping arms. We propose an anti-swing control strategy by adjusting the angle of the transmission line gripping arm’s pitching joint to make the body offset approach zero, and by utilizing the advantages of fuzzy logic in the fuzzy PID algorithm compared with the traditional PID algorithm, it can adaptively avoid the occurrence of robot swinging phenomena. The experimental results of obstacle-crossing experiments under no wind and wind turbulence conditions indicated that the proposed anti-swing control method in this study can effectively keep the body offset to within 3 mm. Compared with the methods of not using anti-swing control and using traditional PID anti-swing control, in the absence of wind effects, the peak values of body offset were reduced by 96.53% and 18.85%, respectively. Under the influence of wind turbulence, the peak values of body offset were reduced by 97.02% and 27.12%, respectively. The effectiveness of the anti-swing control method proposed in this paper has thus been verified.