This paper introduces the methodology of the dimensional synthesis for a 3UPS-PRU parallel robot. The dimensional synthesis of the 3UPS-PRU parallel robot is proposed considering the maximum input velocity of actuating joints as the objective function and constraints on the installation dimension, robot dimension, joint rotation angle and interference. The objective of the dimensional synthesis is to minimize the maximum input velocity of actuating joints when the moving platform translates along the z-axis in the maximum linear velocity and rotates about an arbitrary axis in the maximum angular velocity in the desired workspace. The constraint on the robot dimension is included in the dimensional synthesis of the 3UPS-PRU parallel robot when pursuing the kinematic property to meet the miniaturization principle with the reduced building cost. An example of the dimensional synthesis of a 3UPS-PRU parallel robot is presented with the maximum linear velocity and angular velocity required for the moving platform in the desired workspace.