The developed history of computational geophysical fluid dynamics is simply reviewed and its research progress and latest developing direction is briefly introduced. For the computational stability of linear evolution equation, the condition of CLF for judging the computational stability of initial value problem is introduced. The Fourier method and heuristic stability theory for the analysis of the computational stability criterion of the difference scheme of linear partial differential equation are also briefly introduced. Furthermore, the GKS theory for judging the initialboundary value problem of linear evolution equation is emphatically discussed. For the computational stability of nonlinear evolution equation, the contents are: the mechanism of computational disorder and instability, the method for solving instability, the construction of instantaneous square conservation scheme, the design of implicit and explicit complete square conservation scheme and the computational stability of forced dissipative nonlinear evolution equation. In the near future progress of computational geophysical fluid dynamics, the relationship between the computational stability and the initial value of nonlinear evolution equation and the construction of explicit quasicomplete square conservation scheme of forced dissipative nonlinear evolution equation are emphatically presented. A brief discussion is given to the problems that needs further study of computational geophysical fluid dynamics. The presentation of the research has undoubtedly guidance for the study of computational geophysical fluid dynamics and the development of atmospheric and oceanic model.