In order to control a class of nonlinear chemical process described by Hammerstein model subject to input constraints and bounded disturbances, a robust model predictive control (MPC) strategy consisting of two steps was proposed. In the first step, the case that the system state cannot be fully measurable was considered and the intermediate variable was determined by the robust output-feedback MPC method. To handle the disturbance, the quadratic boundedness technique was adopted to design the formula for updating the bound of the estimation error on-line so that the system was bounded convergence. In the second step, the actual control input with constraints satisfaction was obtained by a solving non-linear algebraic equation group and desaturation. The polypropylene multi-grade transition control was stimulated to illustrate the effectiveness of the approach. Results show that by applying the proposed two-step MPC, the recursive feasibility of the optimization problem and robust stability of the closed-loop system are both guaranteed.