Abstract: By utilizing the method of quantum mechanics,a time dependent solution of the coupled air-sea stochastic dynamic model is obtained accurately.The solution reveals that the air-sea system is in a way of Brownian motion if the system is of basic state,herefrom the standpoint of Hasselmann's stochastic climate model is proved theoretically.If the system is of the first excited state,the system is in a way of decay with time or in a way of periodic oscillation with a main period of 2.3 years in certain conditions of the system. Finally,the solution is applied to study the effect of doubling CO2 on the climate.