This paper discusses a nonlinear Model Predictive Control (MPC) algorithm for multiple-input multiple-output dynamic systems represented by cascade Hammerstein-Wiener models. The block-oriented Hammerstein-Wiener model, which consists of a linear dynamic block embedded between two nonlinear steady-state blocks, may be successfully used to describe numerous processes. A direct application of such a model for prediction in MPC results in a nonlinear optimisation problem which must be solved at each sampling instant on-line. To reduce the computational burden, a linear approximation of the predicted system trajectory linearised along the future control scenario is successively found on-line and used for prediction. Thanks to linearisation, the presented algorithm needs only quadratic optimisation, time-consuming and difficult on-line nonlinear optimisation is not necessary. In contrast to some control approaches for cascade models, the presented algorithm does not need inverse of the steady-state blocks of the model. For two benchmark systems, it is demonstrated that the algorithm gives control accuracy very similar to that obtained in the MPC approach with nonlinear optimisation while performance of linear MPC and MPC with simplified linearisation is much worse.