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3-DOF parallel mechanism (PM) is widely used in manufacturing since, which is simple and flexible. According to the PM design theory and method based on the position and orientation characteristic (POC), a novel two-translation and one-rotation (2T1R) asymmetric spatial PM without parasitic motion, RPa‖3R-R+RSS, was designed. Firstly, the topology characteristics of the PM were analyzed, including POC of the platform, the DOF and the coupling degree (к), which demonstrated that the PM was zero coupling degree and of partially decoupled motion. Secondly, the analytical modeling of the forward and inverse position solutions was derived by using kinematics method based on ordered SOC units. In addition, the direct and inverse kinematics were verified by numerical methods using Matlab. And then the shape and size of workspace and rotation capability of the PM were analyzed. Finally, conditions of singularity of the PM were discussed, and velocity and acceleration of the PM were calculated and simulated. This PM had advantages of simple structure and easy manufacturing, which can be used to convey, assemble and position operations in manufacturing. The analysis results indicated that the kinematics analysis of the PM was not complicated, the rotation capability was strong and the performance of dynamics was better.