This article presents the design and fabrication of a monolithic compliant microgripper. This research has mostly focused on the process of design, the finite element analysis, the fabrication method and use of a genetic algorithm method to solve the nonlinear kinematic equations and estimate the proper dimensions of the design. This new architecture of the microgripper enables it to apply a variable force to a wide range of micro-objects handled in microassembly, micromanipulation and also in biomedical applications such as artificial fertilization. The microgripper was designed to be normally open. Two shape memory alloy actuators close the jaws. To achieve the tasks, the most proper size has been considered to be 8 x 8 mm, with thickness of 250 µm. Polyethylene terephthalate has been used as the structural material. It is not brittle and is less sensitive to shock compared with silicon-based grippers; furthermore, its fabrication cost is less and it does not lose precision.