This paper proposes the design and simulation of a passive type of constant-force microgripper which is based on microelectromechanical systems (MEMS). The constant force is realized by making use of a combination of inclined bistable beams and straight leaf flexures. The constant output force is activated when the input displacement reaches in the range between 10 μm and 20 μm. Analytical model is built to facilitate the structure design of the gripper. Finite element analysis (FEA) simulation study is conducted to verify the theoretical model and to predict the performance of the microgripper. Owing to the large force and displacement, Z-shaped beams are selected as electrothermal actuator to drive the gripping arm. Results show that a gripping displacement of 39 μm can be achieved with an input voltage of 5 V.