The stiffness and elastic deformation of a 3-leg 5-DoF parallel manipulator (PM) with asymmetrical structure and composite active legs are studied systematically. First, a 3-leg 5-DoF 2SPS+PRRPR PM with asymmetrical structure and composite active legs is constructed and its structure constraint characteristics are analyzed. Second, the formulae are derived for solving the elastic deformation and the compliance matrix of the asymmetrical active legs, an asymmetrical stiffness matrix is established for this PM and the elastic deformations of moving platform and legs are solved and analyzed. Finally, a finite element (FE) model of this PM is constructed and the simulation solutions of the elastic deformations of the moving platform are obtained and analyzed. The analytic solutions of the elastic deformations of this PM are verified by its FE simulation solutions.