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The parallel manipulator with three-dimension translation and one-dimension rotation (in short, 3T1R) has wide requirements in processing technology, such as high-speed catch, positioning assembly, transportation. A novel 3T1R parallel manipulator was presented based on the theory of position and orientation characteristics (in short, POC). A complete type synthesis of parallel manipulator that can perform 3T1R motion was made based on the theory of POC. Then, one topology was selected from the different possibilities of parallel manipulators after imposing some practical requirements. The selected parallel manipulator was composed of four identical arms and a single platform, and the composite parallelogram structure in each arm brought in better limb stiffness. The parallel manipulator had characteristics of full symmetry, fold ability, good stiffness, large work space, and so on. In addition, the forward and inverse displacement equations of the parallel manipulator were derived, which had great importance when implemented in velocity control. The inverse position equation had 16 solutions at most, and the forward position equation only had 8 solutions at most. Finally, the solution algorithm of the forward displacement equations was given, and a numerical example was provided to confirm the efficiency of the solution procedure. The research results had a reference value for follow-up studies of the new manipulator and its application.