Structural topology optimization with the use of finite element analysis has been studied and applied in the design of three dimension micro-positioning. A mathematical model of topology optimization for three dimension micro-positioning, which has displacement objective considering stress constraints is proposed. Sensitivity method and OC method are applied to solve this topology optimization problem. Checkboard patterns and mesh-dependency generated in optimization process, and filtering approach is adapted to solve these problems. In the end, a three dimension micro-positioning topology optimization design is presented to show the feasibility of the proposed approach, and the simulation by ANSYS proves the good performance of the micro-positioning. 