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In this paper a robust model predictive control (MPC) for constrained discrete-time nonlinear system with additive uncertainties is presented. This controller uses a terminal cost, terminal constraint and nominal predictions. The terminal region and constraints on the states are computed to get robust feasibility of the closed loop system for a given bound on the admissible uncertainties. Furthermore, it is proved that the closed-loop system is input-to-state stable with relation to the uncertainties. Therefore, the closed-loop system evolves towards a compact set where it is ultimately bounded. In case of decaying uncertainties, the closed-loop system is asymptotically stable. The convergence of the closed loop system is guaranteed despite the suboptimality of the solution.