In this paper, a model predictive control (MPC) design method is proposed for Hammerstein systems with multivariable nonlinearities. Iterative inversion is introduced such that classical linear MPC design can be used. The condition for which the numerical inversion is guaranteed to converge is derived. From this condition, the input space at which the nonlinear function is invertible can be obtained, which poses extra input constraints for MPC design. The overall constraints are transformed and approximated by a set of linear constraints by means of convex hull construction. Illustrative examples are presented to demonstrate the effectiveness of the proposed control method.