A 6UPS-3UPS/UPU-R parallel motion simulation platform mechanism with the capacity to carry heavy load was presented. Driven by electro-hydraulic hybrid, the mechanism could compensate the gravity of the load. Calculation formulas of the force acting on moving platform exerted by the balance platform and the motor torque were obtained by analyzing the dynamics of the mechanism. The balance efficiency was presented, and then the influence of relevant parameters of the balance branches on balance efficiency was researched. The effects of hydraulic cylinders on the force of moving platform and the drive of electric cylinders were got. The numerical analysis indicates that the balance hydraulic cylinder can decrease the motor torque effectively, and the parallel motion simulation platform mechanism can satisfy the application requirements of high precision and heavy load with low manufacturing cost.