The microgripper plays an important role in the micro-assembly system, which directly contacts the target object. The working range of a normally open or normally closed gripper is limited. In this paper, a monolithic flexible microgripper with dual piezoelectric-actuation modes is presented, which combines the characteristics of normally open and normally closed grippers. It has the advantage of enhancing the adaptability of the gripper for grasping objects of different sizes. Different types of bridge mechanisms and parallelogram mechanisms are used in the displacement amplification structure of the gripper. Based on the kinematics model, the displacement magnification ratio of the gripper is analyzed. The crucial structural parameters affecting the magnification were selected to complete the structural optimization of the gripper. Then, the performance of the optimized gripper is verified by performing finite element analysis simulation study. Finally, a prototype microgripper is built and a series of experiments has been performed. The working stroke, natural frequency, and two working mode of the purposed microgripper have been tested and verified. The experimental results reveal that the designed gripper has a large clamping range (860.81 micrometer) and a sufficient-high natural frequency (401 Hz).