This paper proposes an Autonomous Welding Mobile Robot (AWMR) used in shipbuilding and large spherical tank welding and its control method. In this method, both the moving and rotating velocity of the mobile platform and the cross slider were controlled simultaneously. The stability of control method was proved through the use of a Liapunov function. Although any set of positive parameters makes the system stable, a condition on the parameters for the system being critically damped for a small disturbance is obtained through linearizing the system's differential equation. In the simulation, we analyzed line and circle-line tracking problem. And the tracking responses with and without velocity limited is also presented. It is shown that the output responses represent non-oscillatory property and effectiveness of the tracking method.