The inverse solution equation set is established according to the mechanism and constrained characteristic of 6- PTRT parallel robot,and the kinematics forward solution equation set is established.Through the further study of the parallel mechanism,the forward solution equations are reduced by six- dimension to three- dimension by using the mechanism own characteristic. The three- dimensional forward solution equations is transformed into solving the optimization problems,and the forward solutions are calculated by using PSO algorithm. The correctness of the mathematical model is verified by comparing between the experimental results and simulation results. This method has the advantages of high efficiency,easy convergence,doesn’t depend on the initial value,and the theoretical basis for the real- time control of 6- PTRT parallel robot is provided.