This paper proposes a robust predictive control approach for additive discrete time uncertain nonlinear systems. The controller design is characterized as an optimization problem of the "worst-case" objective function over an infinite moving horizon. A sufficient state feedback synthesis condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time step. A few simulation examples are exploited to illustrate the effectiveness of this method. Among them are two typical CSTR problems. (c) 2013 Elsevier Ltd. All rights reserved.