In this paper, Magnus Series Expansion Method, which is based on Lie Groups and Lie algebras is proposed with different orders to solve nonhomogeneous stiff systems of ordinary differential equations. Using multivariate Gaussian quadrature, fourth (MG4) and sixth (MG6) order method are presented. Then, it is applied to nonhomogeneous stiff systems using different step sizes and stiffness ratios. In addition, approximate and exact solutions are demonstrated with figures in detail. Moreover, absolute errors are illustrated with detailed tables.