Abstract A kinetic model based on Michaelis–Menten equation was developed to simulate the dye decolourisation of Reactive Black 5 (RB5), Reactive Blue 114 (RB114), Reactive Yellow 15 (RY15), Reactive Red 239 (RR239) and Reactive Red 180 (RR180) dyes by commercial laccase. The unusual kinetic behavior of some of these reactions suggests that the kinetic model must consider the activation of the laccase-mediator system. Several reactions at different concentrations of each dye were performed in batch reactors and time courses were obtained. A LSODE code to solve the differential equation obtained from the batch reactor was combined with an optimization Fortran program to obtain the theoretical time courses. The time courses obtained from the developed program were compared with the experimentally obtained ones to estimate the kinetic constants that minimized the difference between them. The close correlation between the predicted and the experimental results seems to support the reliability of the established models.