A class of El Nio/La Nia-southern oscillation (ENSO) stochastic disturbed model is considered. Firstly, using the special method of undetermined coefficients, the exact solution of the non-disturbed ENSO model is obtained. Then the approximate solutions of stochastic disturbed ENSO model are constructed by using the asymptotic theory and method. And it is illustrated with example that the asymptotic solutions have the better degree of accuracy.