The main feature of hybrid-driven linkage is the combination of the motion of a large constant velocity motor with that of a small servomotor via a two-degrees-of-freedom mechanism. Thereby, the hybrid-driven linkage can provide for programmable motion output. In the present study, a mechanical drawing press driven by a hybrid mechanism was optimized for displacement and velocity. An analysis of forward kinematics and an optimum model are presented. The actual displacement curves of the slider can approach the ideal ones by means of a two-step optimization. The dimensions of the linkage and the motion rules of the servomotor were optimized. The flexible features of the hybrid-driven drawing press are effectively demonstrated by three optimum examples. The optimum results validate the advantages of the hybrid-driven seven-bar mechanical press, such as its flexible slider speeds and adjustable strokes for drawing operations. By properly designing the input motion of the servomotor, the slider can pass through the desired trajectories.