Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm. High-order sliding mode control is a valid method used in the nonlinear tracking control system, which can eliminate the chattering of sliding mode control. Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control. To address the fast convergence and robustness problems of tracking target, the tracking mathematical model of WMR and the target is derived. Based on the finite-time convergence theory and second order sliding mode method, a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time. At the same time an observer is applied to substitute the uncertain acceleration of the target, then a smooth nonlinear tracking algorithm is proposed. Based on Lyapunov stability theory and finite-time convergence, a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method. The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.