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, here-from 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.