This paper presents a decentralized motion control method of welding mobile manipulators which use for welding in many industrial fields. Major requirements of welding robots are accuracy, robust, and reliability so that they can substitute for the welders in hazardous and worse environment. To do this, the manipulator has to take the torch tracking along a welding trajectory with a constant velocity and a constant heading angle, and the mobile-platform has to move to avoid the singularities of the manipulator. In this paper, we develop a kinematic model of the mobile-platform and the manipulator as two separate subsystems. With the idea that the manipulator can avoid the singularities by keeping its initial configuration in the welding process, the redundancy problem of system is solved by introducing the platform mobility to realize this idea. Two controllers for the mobile-platform and the manipulator were designed, respectively, and the relationships between two controllers are the velocities of two subsystems. Control laws are obtained based on the Lyapunov function to ensure the asymptotical stability of the system. The simulation and experimental results show the effectiveness of the proposed controllers.