An impact of climate change due to global warming will be one of the most severe environmental issues in the 21st Century. In this paper, an efficient numerical solver for a global climate model is developed and presented as a useful and powerful tool for global warming analysis. The model mainly consists of four parts; i.e., atmosphere and ocean dynamics, atmosphere and ocean physics, land surface and sea ice. Major features of this model, which are different from the existing climate models, are: (1) the atmosphere and ocean are treated as a stratified fluid in the dynamics submodel; and (2) the model is computed in the time-space segment using the time-space method, a highly-efficient numerical method for integrating transient parabolic-like equations.