Abstract: The degree of freedom of a 4-SPS/CU parallel mechanism which can perform three-dimensional rotations and translation along Z axis was analyzed based on the screw theory, and concluded that this parallel mechanism was a non-overconstrained mechanism. By the dismantle-bar method, the static equilibrium equations of the mechanism were set up. The equations' number are more than the unknown variables in the static equilibrium equations (belong to overdetermined equation), and the number of redundant equations were equal to the passive degrees of freedom. All of the forces/torques of each component of the mechanism was obtained by solving the static equilibrium equations which got rid of the redundant equilibrium equations corresponding to passive degree of freedom. The simulation curves of the driving force and constraint reactions were given with change of the mechanism's position and posture. It was confirmed that the mechanism had better carrying capacity than other 4-DOF parallel mechanism without the driven chain. The research results could provide the statics analysis method for the application of engineering and structure design.