The nonstationary behaviors of complex system and their applications to the climate prediction present a significant and forward-looking study. Up to now, its importance is not yet well understood. In reality, climate is just a normal nonstationary system. However, almost all the current theories for climate prediction, including the ones in statistics and nonlinear science, are based on one assumption that the process is stationary which is contrary to the nature of the climate process. Probably, this contradictory is an important cause resulting in the climate prediction being at a low reliability level. Therefore, it is theoretically important in climate prediction to start with how to reduce the nonstationary degree of time series. In this paper, support vector machine (SVM) method based on an idea of dimension raising is presented to study the time series prediction analysis, and prediction experiments are performed using some nonstationary time series from the Lorenz model and logistic system with changing control parameter, as well as two realistic climatic time series. The prediction results suggest that the SVM method can perform well in predicting nonstationary time series, which may be due to that the SVM method can map the input space into a higher dimensional feature space through nonlinear mapping and can reduce to some extent the nonstationary degree of the system.