To forecast the dynamic responses of closed high-speed precision press accurately, a 3-degree-of-freedom (DOF) dynamic model of mass-spring damping is proposed in this work. This model operates by using the centralized parameter method. Considering the instantaneity of impact load, we employ impulse simulation to simulate the periodic impact working conditions of a JF75G-200 high-speed press using both 2-DOF and 3-DOF models. Simulation data on the dynamic responses of the press are acquired and compared with the results from on-site measuring. The proposed 3-DOF dynamic model of mass-spring damping has been proven by our simulation and test to be reliable as well as effective for detecting the dynamic responses of the press.