In this paper a model-based predictive control (MPC) algorithm is presented for Hammerstein-Wiener systems. This type of system consists of a linear dynamic block preceded and followed by a static non-linear block. These systems appear useful in modelling several non-linear processes encountered in industry. Directly using such a model in a MPC algorithm will in general lead to a non-linear optimization problem due to the static non-linearities. This can be avoided by exploiting the structure of these models. In this paper the non-linearities are transformed into polytopic descriptions. This procedure enables one to use robust linear MPC techniques for cont rolling these systems. In such a way a convex optimization problem is retained. For the presented MPC algorithm, which is stat ed as an optimization problem subject to linear matrix inequalities, nominal closed loop stability is proven. In two examples it is shown that by means of transforming the non-linearities into polytopic descriptions, as done in the presented MPC algorithm, a better tuning of the input-out put behaviour of the plant is obtained, compared to removing the static non-linearities from the control problem by an inversion, a technique often used for these systems.