A novel 5-DoF parallel manipulator (PM) with two composite rotational/linear active legs is proposed and its kinematics and statics are studied systematically. First, a prototype of this PM is constructed and its displacement is analyzed. Second, the formulas are derived for solving the linear/angular velocity and acceleration of UPS composite active leg. Third, the Jacobian and Hessian matrices are derived and formulas for solving the velocity, statics and acceleration of this PM are derived. Third, a reachable work space is constructed using a CAD variation geometric approach. Finally, the kinematics and statics of this PM are illustrated and solved. The solved results are verified by the simulation results.