A new 2-UPS-PU parallel manipulator with one translational and two rotational degrees of freedom (DOF) has been proposed in this paper, which has the advantages of high rotational capability and high load carrying capacity, etc. The mobility of the robot is analyzed. The inverse and forward kinematics problems are solved. The velocity and force Jacobian of the new parallel manipulator are given. An effective method for computing this manipulator’s workspace is proposed. The workspace is represented in an ingenious selected cylindrical coordinate system. An optimal dimensional synthesis method is presented to optimize all the parameters of this manipulator for a prescribed workspace with the excellent mechanical performance.