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The 3-PUS-PU compliant parallel mechanism with high precision and high stiffness was proposed. Its kinematic analysis and optimization design were carried out. According to the structure of the flexible hinges and the geometric relations of mechanisms, the motion principle of 3-PUS-PU compliant parallel mechanism was described, and the motion characteristics of the mechanism were analyzed. The kinematics model of the mechanism was established by the closedloop vector method, and the input-output relationship and velocity characteristics of the mechanism were analyzed. Then, the limit angle of flexure hinges was analyzed based on the theory of elasticity. According to constraint conditions and geometric parameters, the workspace of the mechanism was obtained by the numerical search method. According to the work requirements of the mechanism, the performances of positioning accuracy and compact were proposed. Then, the influence of structure parameters of the mechanism on the performances were analyzed. Finally, the particle swarm optimization algorithm was adopted to optimize the size parameters of the mechanism. Compared with the original mechanism, the optimal mechanism was improved by 25% and 81% for positioning accuracy and compactness, respectively. The results showed that the optimal mechanism performance of the kinematics was good. It can provide guidance for the subsequent prototype development.