We investigate the model for an industrial isothermal HDPE slurry reactor. The model, consisting of several nonlinear equations, can be linearized to give sets of linear time invariant state space model. The effectiveness of the linearized model is verified by the numerical simulations. A simple model predictive control scheme is constructed based on the linear state space model. The value of the melt index is obtained from the values of the manipulated and controlled variables generated from the control scheme. The control performance can be evaluated from the comparison between the computed melt index values and measured melt index values. The control scheme shows good tracking performance in the numerical simulations. We believe that the model developed in the present study can be effectively used to predict process variables as well as to control the melt index.