This article proposes a robust model predictive control (MPC) algorithm for the tracking problem of wheeled mobile robots. The robots are subject to bounded disturbances and various practical constraints. Particularly, the incremental input constraint is introduced in the consideration of the safety and comfortability needs in real life. Conditions on the acceleration of the leader robot are derived to guarantee the satisfaction of the incremental input constraint of follower robot. To compensate for the effect of disturbances, a disturbance observer is designed to obtain the estimation of the disturbances, which together with the optimal control input of MPC optimization is contained in the actual control input. Also, a novel quadratic robustness constraint is developed to handle the disturbance estimation error, which allows the designer to balance the initial feasible region and control performance. The proposed algorithm can ensure recursive feasibility, robust constraint satisfaction, and closed-loop stability. Finally, both simulation and experiment results are provided to verify the theoretical properties.