The motion analysis of 3- RRS spherical parallel mechanism is carried out by using the screw theory. The forward kinematics of 3- RRS spherical parallel mechanism is solved by using Newton iterative method. The inverse kinematics model of 3- RRS spherical parallel mechanism is established by using closed loop vector method. The corresponding inverse position solution formula is derived. Eight sets of inverse solutions are obtained. Through the example analysis,the validity of the position solutions of 3- RRS spherical parallel mechanism is verified. The reachable workspaces of 3- RRS spherical parallel mechanism are solved with the help of numerical search method. The reachable workspace diagrams with different structure parameters are drawn by using Matlab software. The variation law of the workapaces is analyzed. The results lay the foundation for the application of 3- RRS spherical parallel mechanism.