A new robust model predictive control (MPC) algorithm is presented for stable, constrained, linear plants that is a direct generalization of the nominally stabilizing regulator presented by Rawlings and Muske. Model uncertainty is parametrized by a list of possible plants. Robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant. Asymptotic stability is demonstrated through a Lyapunov argument. Simulation experiments demonstrate the performance of the algorithm for two example processes.