Research on trajectory tracking control for climbing welding robots holds significant importance in the field of automated welding. However, existing trajectory tracking methods suffer from issues such as jitter and slow speed. In this paper, an improved sliding mode control strategy is proposed based on the self-designed wall-climbing welding mobile manipulator. Firstly, a new adaptive sliding mode control strategy is proposed for the mobile platform based on the kinematic model. By introducing a new approach law, the controller is designed when the distance between the center of mass is unknown. Secondly, regarding the manipulator, we analyze simplified dynamic equations, extract uncertain components, and utilize a CNN for compensation. This compensation strategy is integrated into the sliding mode control law, achieving precise control over the manipulator and effectively resolving issues like slow tracking speeds, large errors, and chattering. The stability of the robot control system is proved by the Lyapunov function. Through simulation analysis and experimental validation, the proposed control method is confirmed to be feasible and superior.