In this paper, a framework which applies the piecewise linear quadratic regulator (PLQR) control based on linear time-varying system was presented to solve the problem of input saturations in the tracking control of wheeled mobile robot (WMR). Based on the Lyapunov method, it is proved that the designed trajectory tracking controller PLQR can satisfy the input saturation condition, and guarantee the stability of closed-loop system. With the Matlab simulation experiments, the results show that the PLQR based wheeled mobile robot has good tracking performance with different initial positions and various reference trajectories.