The motion of multi-link high-speed press drive system was analyzed and the kinematic model of multi-link high-speed press drive system was also established. Some curves including slider displacement curve, slider velocity curve and slider acceleration curve were obtained by using ADAMS based on multi-link high-speed press being designed and the two factors(crank radius and the position of fixed pivot point  H) affecting the slider curves and strokes were studied. Compared with the motion curves of crank-connecting rod mechanism, the multi-link mechanism has the characteristics of small velocity near bottom dead center（B.D.C）and high velocity in return. The results show that it is bad to slider motion characteristics when the crank radius increasing and it has the opposite effect on slider curves when the  length of  OH′s increasing. The results can provide reference for the designing of multi-link high-speed presses.