In this paper a multivariable generalized predictive controller (GPC) for the effective control of a reverse osmosis (RO) unit of a water purification plant of a pharmaceutical industry is designed. By using subspaces methods for identification of dynamic systems a multivariable mathematical model of the plant under study is obtained, whose validation results showed a high adequacy degree. The design of the multivariable GPC controller is performed based on the mathematical model obtained. It is shown that the designed controller allows controlling the RO unit under study with a high accuracy considering different real industrial operation scenarios. The comparative simulation results of the control system with PI (decoupled), DMC and GPC multivariable controllers showed a better performance when the GPC controller is applied.