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A kind of 2-DOF spherical parallel mechanism was presented. Based on the mechanism, a type of wheel-legged mobile robot was developed, which had a simple structure and a good obstacle climbing ability. According to the design theory for parallel mechanisms based on position and orientation characteristic equation and the principle for the coupling degree reducing, a novel 2-DOF spherical parallel mechanism was proposed. The inverse kinematics, workspace, velocity and acceleration model of RUPU-RUPR spherical parallel mechanism were modeled by using analytic geometry method and closed loop constraint equation. The workspace, velocity and acceleration solutions were verified by numerical methods. The dynamic equations of RUPU-RUPR spherical parallel mechanism was also established by Newton-Euler formulation. Given the platform moving rules and external forces, the driving torque of the RUPU joint and the constraints torque of the RUPR joint were calculated. A simulation solution of the dynamic model was given. The results illustrated that the spherical parallel mechanism had a simple mechanical structure and large workspace. The research provided a theoretical base for its kinematics and dynamics and workplaces of this spherical parallel mechanism.