The rate equations are very often to be solved in the simulation and the optimization of the biochemical reaction system. Numerical computations of the equation by the digital computer have been frequently confronted with its stiffness. The computations of the stiff system require a great deal of computation time in comparison with those of the other systems. From this point of view, usual techniques are of no practical use for the stiff systems. The Fowler-Warten method, which is one of the explicit integration formula for stiff system, was modified and applied to the three-step enzymatic reaction. By the present method, the computation of the time-course can be performed with rapidity and small error.