Abstract: Two-dimension non-hydrostatic β-γ meso scale atmospheric model is used to simulate an European cold frontal process in 1987,whose initial fields come from a hydro-static model.The horizontal extension is 2000 km and three different horizontal resolutions 5 km,25 km,and 45 kmare used.The results show:1) It is practical fora meso scale non-hydrostatic model to use non-homogeneous initial fields,withoutan artificial disturbance celladded.2) The initial fields of the distur bed quantity (pressure π'), should fo llow s the principle of hydrostatic balance strictly,other wise it can consul tin greatacceleration,so far as to change the vertical velocity field completely in a shorttime step.3) Non-hydrostatic model with grid length of 5 km can getseveral meso scale convective cells on the front,and the distribution of vertical velocity are similar to the reality,while the model with largerresolutions (25 kmand 45 km) can only describe a wide updraftasso ciated with front.