In this paper, dimensional synthesis of a novel 3-PUU parallel manipulator, which is applied for a parallel kinematic machine (PKM) tool, is proposed. Firstly, kinematics analysis of the parallel manipulator is established, and the inverse solutions of the kinematics are systematically analyzed and geometric description is given. Secondly, the Jacobian matrix is deduced and the kinematic dexterity index and the workspace are introduced. In order to require better dexterity performance and larger workspace, multi-objective optimizations based on non-dominated sorting genetic algorithm II (NSGA-II) are performed in terms of dexterity performance and workspace of the proposed parallel manipulator. By optimizing the design variables including geometric dimensions of the parallel manipulator, the dexterity and workspace of the proposed parallel manipulator have been greatly improved. The analytic results are verified by simulation to show that the parallel manipulator has a good application prospect.