The parameterized dynamic simulation model for a multi-link high precision press has been established in the ADAMS software environment based on the displacement equations. The press being developed is taken as an example to study the slider’s displacement curves, velocity curves and acceleration curves under different crank radius in practice as well as the working angle curves and torque curves. With the crank radius increasing, the started punching angle comes early and the slider’s velocity and acceleration at bottom dead center (B.D.C) decreases significantly which help to improve the accuracy of B.D.C and to lower the torque consumption during stamping. Meanwhile, the increasing of working angle helps to reduce the lateral force acting on the slider, such as the torque required to overcome the inertial forces increases rapidly, the torque needed to overcome the nominal force decreases and the peak of nominal force shifts to the lower left gradually. Results of the research mentioned above are helpful to develop the multi-link high-speed press.