In this paper, robust model predictive control (MPC) is studied for a class of uncertain linear systems with structured time-varying uncertainties. This general class of uncertain systems is useful for nonlinear plant modeling in many circumstances. The controller design is characterizing as an optimization problem of the "worst-case" objective function over infinite moving horizon, subject to input and output constraints. A sufficient state-feedback synthesis condition is provided in the form of linear matrix inequality (LMI) optimizations, and will be solved on-line. The stability of such a control scheme is determined by the feasibility of the optimization problem. To demonstrate its usefulness, this robust MPC technique is applied to an industrial continuous stirred tank reactor (CSTR) problem with explicit input and output constraints. Its relative merits to conventional MPC approaches are also discussed.