Based on the principle of linearized stability proposed by Lyapounov, we investigate the robustness of Majorana zero energy state (MZES), which plays an important role in topological quantum computation. Our study is different from previous works that usually explore the stability of MZES by the numerical test of some special perturbations, our treatment is suitable for arbitrary perturbations. Since our method follows the stability theory of differential equation, the results we obtained are reliable. As an example, we demonstrate it by the stability of MZES in the spin-orbit coupled semiconductor/ superconductor junction, the analytical and numerical results indicate that the MZES is unstable in this system.