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A simple and symmetrical parallel mechanism with three translations is designed according to the theory and method of topological design of parallel mechanism based on Position and Orientation Characteristic （POC） equation. The topological characteristics of mechanism，such as position and orientation characteristic set，degree of freedom and coupling degree，are calculated respectively by POC equation to verify the kinematics characteristics of the mechanism with three translations. The kinematics equation of the mechanism is established，and the analytical expression of positive and inverse kinematics solution of the mechanism are derived，the singularity，workspace and dexterity of the mechanism are studied. Finally，a multi-objective optimization design model is established，with elite retention strategy of rapid and dominate the multi-objective optimization algorithm （NSGA-Ⅱ），the scale synthesis of the structural parameters is carried out，a set of Pareto optimal solutions are obtained by optimization. The results show that the workspace volume and global dexterity can’t be maximized at the same time. Pareto optimal solution can be selected according to the actual needs to meet the needs of the two goals.