In this paper a new asymmetric 3-translational (3T) parallel manipulator, i.e., RPa(3R) 2R+RPa, with zero coupling degree and decoupled motion is firstly proposed according to topology design theory of parallel mechanism (PM) based on position and orientation characteristics (POC) equations. The main topological characteristics such as POC, degree of freedom and coupling degree are calculated. Then, the analytical formula for the direct and inverse kinematic are directly derived since coupling degree of the PM is zero. The study of singular configurations is simple because of the independence of the kinematic chains.