A novel 3—PRRR three-dimensional translational parallel mechanism was proposed. Its Jacobian matrix was constant, when its prismatic pairs were chosen as the actuators. The degrees of freedom of the parallel mechanism was analyzed based on screw theory. The forward/inverse kinematic solution models were established to obtain its workspace by the vector method. Jacobian matrix of the mechanism was solved by the main twist screw and transmission wrench screw. Then, the curves of the output speed and force were drawn. According to the figures, the curves were completely coincident in different poses when the input parameters were certain. Thus, the conclusion that the Jacobian matrix of the 3—PRRR parallel mechanism kept constant was verified. On this basis, the transmissibility performance of the mechanism was further analyzed in order to obtain relationship between transmission power and angle β (the angle between axis of the prismatic pair and its nearest pairthe revolute pair ) of each limb. Finally, another important conclusion was got. It can be expressed as: when the input power was definite and invariant, the transmission power of the mechanism was decreased with the increase of β. Comparison was made between output speed and force curves in two cases that β were equal to 0° and 30°, the transmissibility performance of the mechanism varied with β and the former was better than the latter. Similarly, after the transmissibility performances with other values of β were analyzed, the performance was optimal when β was 0°.