It is difficult for 3PRS parallel mechanism to control due to its strong coupling and susceptibility to disturbances. Thus the decoupling and control strategies of the mechanism were studied. Firstly, the inverse kinematics model of the mechanism was established, the kinematic equations were deduced between the position and pose of the moving platform and the heights of the input sliders. The kinetic and potential energies of the motion component within the mechanism were analyzed, the Lagrange dynamic equations for the 3-PRS parallel mechanism were obtained. The driving forces on the position and pose of the moving platform in both zero-gravity and normal gravity environments were further investigated. The theoretical model and numerical simulation were performed and the consistency and accuracy of the dynamic model were confirmed. The state-space equations based on the inverse dynamics model were formulated, and the Lie derivative expressions for the 3-PRS parallel mechanism were studied to enable feedback linearization decoupling of the state-space equations. The simulation analysis was conducted on the decoupled statespace model. The experiment platform of 3-PRS parallel was set up to verify the effectiveness of the proposed method. The controller for the 3-PRS parallel mechanism was designed on the basis of the complete decoupling and the integral sliding mode control. The effectiveness of the controller was validated through the simulation experiments. The results indicated that the designed controller can not only decouple its dynamical model but also can track the expected trajectory under the presence of disturbances and time-varying input driving forces, which made the system possess with strong robustness.