The overhead transmission line has a catenary shape, which has great influence on the dynamic characteristics of an inspection robot walking along the line and may even cause the walking-wheel to fall from the line. Compared with other similar inspection robots, the unique structure of the dual-arm inspection robot with flexible-cable is introduced. Taking the dual-arm inspection robot with flexible-cable walking along the uphill section of the line as an example, the force states of the robot when it works at acceleration, uniform speed, deceleration, and stopping were studied in detail. The corresponding force balance equations were established, and the walking-wheel torques in each working state were solved. The working states of the robot walking along the catenary shape line were simulated using ADAMS software. Simulation results show that the walking process of the robot is stable, the walking-wheels have good contact with the line, and the forces of two walking-wheels are almost balanced, which enables the robot to have good adaptability and climbing ability for the line. The prototype test that the robot walked along the line was carried out. The results of the simulation and prototype test are consistent with the theoretical analysis, so the rationality of robot structure design is verified. In the future, the navigation control and stability of the robot walking along the line will be researched, so that the robot can complete the patrol task in the real environment.