This paper proposes an adaptive controller for partially known system and applies to a two-wheeled Welding Mobile Robot (WMR) to track a reference welding path at a constant velocity of the welding point. To design the tracking controller, the errors from WMR to steel wall is defined, and the controller is designed to drive the errors to zero as fast as desired. Additionally, a scheme of error measurement is implemented on the WMR to meet the need of the controller. In this paper, the system moments of inertia are considered to be partially unknown parameters which are estimated using update laws in adaptive control scheme. The simulations and experiments on a welding mobile robot show the effectiveness of the proposed controller.