The paper concerns the receding horizon predictive control of constrained nonlinear systems and presents an algorithm which relies on the online solution of a simple linear program (LP). Use is made of a finite control horizon in conjunction with a terminal inequality constraint and a predicted cost that includes a terminal penalty term. The optimization procedure is based on predictions made by linearized incremental models at points of a given seed trajectory and the effects of linearization error are taken into account to give a bound on the predicted tracking error. The algorithm is posed in the form of an LP and the proper selection of the terminal penalty term of the predicted cost guarantees the asymptotic stability. The results of the paper are illustrated by means of a simple example.