The work aims to check whether it has the concomitant motion and analyze the positive and inverse solutions of the position and pose with respect to UPS+UPR+S parallel mechanism with two degrees of freedom. The expression of the corresponding vector was obtained by rotating the change matrix, and the constraint equation was established to verify whether there was concomitant motion. The positive and inverse solutions of the mechanism were analyzed, and part of positive solutions of the mechanism were obtained by genetic algorithm and mutually verified with the inverse solutions. An example was given to validate the analysis, and the best individual, the best fitness, the diversity value and the score of individuals of each generation were obtained. There was no concomitant motion in the mechanism, the difference between positive solution and inverse solution was small, and the data could be consistent with each other. The best individuals obtained by positive solution were -0.267 and 0.31, subsequently mutually verified with the inverse solution. The optimal fitness decreased gradually, and the score of each generation and the score of individuals of each generation were obtained. There is no concomitant motion in the mechanism, and the performance is good. As the positive and inverse solutions coincide with each other, the correctness of the positive and inverse solutions can be proved.