In order to achieve the precise and offset-free tracking of the positioning mechanism in precision manufacturing for the time-varying trajectories within the allowed error bound, an error-bounded and offset-free model predictive control (EOMPC), based on robust control invariant(RCI) sets, is proposed for constrained uncertain systems. Firstly, for the purpose of removing the steady-state errors caused by the disturbances, an augmented system that contains the system output, estimated state, and estimated disturbance, is constructed and used as the prediction model to improve the prediction accuracy. Then, on the basis of the augmented system and trajectory model, an iterative procedure that can be terminated in finite steps is presented to obtain the RCI set, which is used as the state constraints in an optimal control problem(OCP) to promise the error-bounded tracking. A numerical optimization scheme that can be executed online is then given for the real-time performance of the OCP. Finally, the effectiveness of the method is illustrated on the maglev positioning system.