This paper presents the results of applying POD (Proper orthogonal decomposition) and predictive control techniques to the control of a non-isothermal tubular reactor. The control goal is to keep the operation of the reactor around a desired operating condition in spite of the disturbances in the feeding flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles the nonlinear PDEs (Partial Differential Equations) that model the reactor are linearized, and afterwards the resulting linear PDEs are discretized in space giving as result a high order linear model. Then a reduced order model is found by means of the POD technique which makes possible the design of an MPC controller for rejecting the disturbances that affect the tubular reactor.