The work aims to design a parallel mechanism which is suitable for the sorting and packaging of the package required to adjust its attitude. In this paper, the parallel mechanism with 2T1R motion mode was synthesized based on the displacement manifold theory. The screw theory was used to analyze the DOF characteristics of the motion mode of this new mechanism in general configuration, and the feasibility of selecting the drive pair of its branched chain was analyzed. The new parallel mechanism could realize the 2T1R motion mode with variable rotation axis. The motion mode of the proposed mechanism is in line with the design expectation, and enables the mechanism to move in a plane and rotate with a variable rotation axis which forms a one-dimensional spherical surface. In packaging and sorting products with complex shape, it may be necessary to adjust the spatial attitude of the products. The parallel mechanism with 2T1R motion mode with variable rotation axis can be applied under this working condition.