The continuous adsorption recycle extraction (CARE) process is an innovator system of enzyme purification with large potential of industrial application, firstly proposed by [Pungor, E., Afeyan, N. B., Gordon, N. F., Cooney, C. L. (1987). Continuous affinity-recycle extraction - a novel protein separation technology. Biotechnology, 5 (6), 604.] The CARE is originally constituted by two stages, adsorption and desorption, each one being approximated by a perfectly mixed reactor. The adsorption stage is by affinity and the desorption stage takes place due to changes in some properties of the system, as pH for instance. The process works in a continuous operation mode with an adsorbent recycle. A washing intermediate stage was included in the original CARE process and this is the process studied in this work. In order to achieve the goal of this work, a representative mathematical model was developed using the kinetic laws and the mass balance for each component in the system stages. The adsorption and desorption kinetic parameters for the lisosyme enzyme were obtained in the literature. There are some difficulties to control the system, such as strong interaction among the input and output variables, non linearity and inverse response. The concentration of enzyme in the liquid phase of two stages of the process is controlled by a dynamic matrix control (DMC) multivariable predictive controller. To carry out this task, the controller DMC manipulates the flowrates of the fermented feed of the desorption stage and of recycle stream of the process. The existence of the restriction of the fermented flowrate, in the adsorption stage, is solved through the strategy of switching of the fermented and recycle flowrate. The control actions are taken in values that guarantee the linearity of the system around the steady state operation point. The simulation results in closed loop of this predictive control system showed an excellent performance.