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Three degrees of freedom parallel manipulator 3-PUS-UP with a properly constrained passive limb was taken as the research objective. Inverse kinematics solution equations were formulated with closed vector method, and a Jacobian matrix of parallel driving part was obtained considering the influences of driving chains, constraint chain and parasitic motion of moving platform. Further, a Jacobian matrix of UP limb of serial part was acquired by adopting the D—H method. Combining the relation between the driving equations with constraint equations, a complete Jacobian matrix of the 3-PUS-UP parallel manipulator was constructed and verified by simulation analysis on the basis of the previous kinematical model. Simultaneously, kinematic dexterity and stiffness were introduced to evaluate the kinematic performance, and distribution atlas of the kinematic dexterity and stiffness in the workspace were drawn and researched. The optimum regions of the kinematic dexterity in the reachable workspace were defined and calculated. The research results show that this 3-PUS-UP parallel manipulator has good kinematic dexterity and stiffness performance.