Abstract: The magnetosphere is outermost layer of the geospace. Interaction of the solar wind with the magnetosphere is one of the key links among the space weather chain process from the Sun to Earth, thus becomes one of the key issues in space weather study. The characteristics of the geospace, including time-dependent, multiple components, and non-linearity, make the traditional analytic study very difficult. Numerical simulations as new means to investigate the coupling system, has played an important role in recent decades. The global MHD simulation about the magnetosphere started in 1970s, and limited to 2D initially. Since the intrinsic 3D characters of the magnetosphere, 3D MHD simulations thrived in 1980s. This paper briefly illustrates the characteristics of the 3D global magnetosphere MHD simulations, and their current status. The framework of the 3D global MHD magnetosphere simulation, and its application to the interaction of interplanetary shocks with the magnetosphere, large-scale current systems, reconnection voltage and cross polar potential drop, K-H instability in the magnetopause etc. are presented.