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A kind of 2RRPaR+PPaP three translational space parallel mechanism is designed, and the forward and inverse position solutions equation and Jacobi matrix of the mechanism are derived. The optimization mathematical model is set up with the optimization goal of workspace and global dexterity. Based on the maximum number of scatter points in the workspace and the maximum dexterity, the differential evolution algorithm is used to optimize the design and get the optimal parameters of the mechanism. By comparing the workspace and dexterity of the mechanism before and after optimization, the results show that the motion performance of the optimized mechanism has been greatly improved, which laid the foundation for the design and application of the mechanism.