The paper aims to design a planar 2-DOF compliant parallel mechanism with the topology optimization technology to make it have kinetic characteristics at the micron level. The kinetic characteristic was analyzed according to the loading situation of planar 2-DOF parallel prototype mechanism. The kinetic differential Jacobian matrix of planar 2-DOF compliant parallel mechanism was built based on isomorphic closed vector mapping principle to show the kinematic relations of the joints from input to output in multiple DOF compliant parallel mechanism. In this paper, the optimization model of rational approximation of material properties for planar 2-DOF compliant parallel mechanism was built, which defined the compliance as the optimization objective function, the differential kinetic Jacobian matrix as kinetic condition and the material volume ratio as constraint condition. The Moving Asymptotes Method was used to solve the optimization problem. For the configuration of planar 2-DOF compliant parallel mechanism after optimization, its displacement in x and y direction was ?0.0089 mm and 0.0053 mm; however, the theoretical displacement in x and y direction was ?0.0031 mm and 0.0067 mm. Results showed that the differential kinetic characteristics of planar 2-DOF compliant parallel mechanism optimal configuration is consistent with its parallel prototype mechanism, and the positional accuracy is achieved at the micron level.