Tubular reactors are non-linear and time-varying distributed parameter systems with complex dynamics so that it is difficult to have high performance and safe operation when conventional classic control procedures are employed. In this work, an adaptive controller based on state space approach is developed and tested for the control of a biochemical reactor, using L-Asparaginase attached on the internal open nylon tube. It is shown that the control algorithm is adequate to maintain the system in a specified operational conditions even when significant disturbances takes place as well as the set-point changes. Furthermore, an adequated operational strategy and a good control scheme improved the stability of the system and make the L-asparaginase reactor to be an efficient method in the treatment of leukaemia.