The time-dependent solution of reduced air-sea coupling stochastic-dynamic model is accurately obtainedby using the Fokker-Planck equation and the quantum mechanical method. The analysis of the time-dependent solution suggests that when the climate system is in the ground state, the behavior of the systemappears to be a Brownian movement, thus reasoning the foothold of Hasselmann’s stochastic climatic model;when the system is in the first excitation state, the motion of the system exhibits a form of time-decaying,or under certain condition a periodic oscillation with the main period being 2.3 yr. At last, the results areused to discuss the impact of the doubling of carbon dioxide on climate. The time-dependent solution of reduced air-sea coupling stochastic-dynamic model is accurately obtained by using the Fokker-Planck equation and the quantum mechanical method. The analysis of the time-dependent solution suggests that when the climate system is in the ground state, the behavior of the systemappears to be a Brownian movement, thus reasoning the foothold of Hasselmann’s stochastic climatic model; when the system is in the first excitation state, the motion of the system exhibits a form of time-decaying, or under certain conditions a periodic oscillation with the main period being 2.3 yr. At last, the results areused to discuss the impact of the doubling of carbon dioxide on climate.