In this work, a hybrid block method based on the four-step Adams-Moulton scheme specifically tailored for solving stiff control problems has been presented. Tests for\ convergence and stability are conducted to verify the validity of the method. Comparative numerical examples are used to demonstrate the level of accuracy exhibited by the new method over the analytical process. The findings indicate the method’s consistency, zero– stability, and A(α)–stability characteristics, and therefore, suitable for practical applications to stiff dynamical systems in operations research. Numerical results are compared with the exact solutions, and indicate a good level of accuracy.