This paper investigates the trajectory tracking control issue for linear parameter-varying (LPV) system of wheeled mobile robot (WMR) with actuator fault and constraints, where a time-varying intermediate estimator (TVIE)-based fault-tolerant model predictive control (MPC) method is proposed. A new estimation-based predictive model is designed by introducing the estimations of error state and fault from the TVIE. Moreover, compared with the existing traditional IE or extended state observer(ESO), the estimation performance of TVIE whose gain is optimized online based on an objective function is better. To guarantee stability and recursive feasibility, the bimodal MPC strategy is used, where a terminal penalty and a terminal constraint are included. Finally, the effectiveness and superiority of the proposed approach is illustrated by two experiments.