Parallel mechanism is difficult to be controlled, because of its strong nonlinearity and complex control process, and its accuracy can not meet the working requirements. This work took a three-degree-of-freedom rigid-flexible coupled parallel robot as the research object, established a simplified space structure model of a robot and the tree model of a multi-body system, used the transfer matrix method of the multi-body system to study the Kinetics and the state space of the robot, and used the Hankel model reduction for the state space. The LQR control and the genetic algorithm (GA)-optimized LQR control were designed, and the working conditions of the robot were simulated and compared. The results show that the LQR control robot based on genetic algorithms (GA) only needs 1 second to enter the steady state. In a steady state, after optimization compared with that before optimization, the maximum displacement of the robot moving platform x, y and z decreased by 24.34%, 13.51% and 1.03% respectively; and the maximum acceleration on the three legs decreased by 26.92%, 33.96% and 35.71% respectively; the maximum control force of each leg decreased by 8.96%, 7.37% and 9.01% respectively. It can be seen that under the optimal control method, the robot has the advantages of fast response, high precision and good stability. Thus the rationality and superiority of the method are fully proved, which provides a theoretical basis for further study of Kinetics performance and control methods of Parallel robots.