Our newly developed CESE MHD model is used to simulate sun-earth connection event with the well-studied 12 May 1997 CME event as an example.The main features and approximations of our numerical model are as follows:(1)The modified conservation element and solution element(CESE)numerical scheme in spherical geometry is implemented in our code.(2)The background solar wind is derived from a 3D time-dependent numerical MHD model by input measured photospheric magnetic fields.(3)Transient disturbances are derived from solar surface by introducing a mass flow of hot plasma.The numerical simulation has enabled us to predict the arrival of the interplanetary shock and provided us with a relatively satisfactory comparison with the WIND spacecraft observations.