A novel 3PUU parallel manipulator considering the mechanism of dexterity property was addressed. Kinematics analysis of the parallel manipulator was established, and the inverse solutions of the kinematics of the 3PUU parallel manipulator were obtained. Based on the previous works, the Jacobian matrix of the mechanism was deduced. The kinematic dexterity index was introduced, and the dexterity of the parallel manipulator of dimensional synthesis analysis was carried out, which laid the foundation for the design of the parallel manipulator mechanism and the further study. The results show that the parallel manipulator robot has a good practical application prospect.