To overcome the low operation efficiency, high labour-intensiveness and high risk in the artificial live-line replacement of insulator strings, a robot for overhead transmission line maintenance was developed. In order to suppress effectively the influences of disturbance signals and uncertainties on tracking precision and stability of the robot mechanical arm motion under high voltage and strong electromagnetic interference, this paper proposed a H control theory-based robust trajectory tracking control method for the robot mechanical arm. Through layering robot control architecture, a dynamic model of mechanical arm basic motion was established by the Lagrange method combined with an armature voltage equation of the joint motor, and the unified dynamic model of mechanical arm different motion was obtained. On this basis, the state-space model of mechanical arm motion error was deduced under disturbances and uncertainties, and thus an H control model for mechanical arm motion was constructed. Subsequently, the H controller for the mechanical arm trajectory tracking control system was solved by linear matrix inequality (LMI) based on the established model, and the asymptotic stability of the mechanical arm motion control system was verified by selecting the appropriate Lyapunov function. The proposed method for such a controller was proved to be of good versatility, strong adaptability and sound expansibility. Finally, simulation results verified the effectiveness of the H controller and field operation tests further validated the engineering practicability of such a control method in macro and micro aspects.