Abstract: An idealized dynamical climate model including seasonal variatons of solar radiation, sea-surface temperature and other climatic elements is designed for an all-ocean planet in this paper.Modeling results indicate: The variations of the equilibria and their sensitivity to changes in external parameters are very large, their values in summer are much larger than those in other seasons. The mean sensitivity of the results for the four seasonal modeling is larger than that of mean annual model, this may be caused by the seasonal variation of solar radiation. In addition, when solar radiation or CO₂ concentration is reduced to a certain value, the bifurcation will present. If it is continuously reduced below this bifurcation point, then catastrophy, "deep freeze", will happen. The values of the external parameters at bifurcation points are much larger in summer than in other seasons. Above results represent that the seasonal variations of physical processes can not be ignored in research of long-term climatic variation.