Microgripper acts as an end-effector in the microassembly system, which completes pick-transport-release actions during the assembly process. Usually, the working space of the microassembly robot is small, and the operating environment is complicated. In addition, the assembled micro-objects are light, thin, brittle, and prone to damage. Thus, the microgripper should be able to provide a compact construction, a suitable clamping range, and safe clamping force for microassembly use. This paper presents the design, modeling, optimization, and simulation of a new piezoelectrically actuated compliant microgripper for microassembly application. The designed clamp has the advantages of large motion displacement and high area usage efficiency. A three-stage amplification mechanism based on bridge-type mechanism and leverage mechanism arranged in series is introduced to achieve a large jaw displacement. The optimization based on response surface analysis has been applied to determine the structural parameters of the amplification mechanism. The displacement amplification ratio of the microgripper is analyzed via the pseudo-rigid-body model approach. Finite element analysis is conducted to evaluate and validate the performance of the gripper. The simulation results indicate that the gripper can achieve a maximum gripping displacement of 545.12 µ m with an area usage efficiency of 370.32 nm/mm, which is better than available designs in the literature.