Robot-assisted minimally invasive surgery (MIS) has shown tremendous advances over the traditional techniques. To improve dexterity and back-drivability of the existing planar remote center-of-motion (RCM) mechanism, on which an active prismatic joint is required to drive the surgical tool move in–out of the patient's body, a two degrees-of-freedom (DOFs) planar RCM mechanism is proposed by constructing virtual parallelograms in this paper. The mechanism can be considered as a generalized double parallelogram; both of the actuated joints are revolute joints. This feature enhances the intrinsic back-drivability of the mechanism. The mathematical framework is introduced first to prove that the mechanism could execute RCM. Then, the inverse kinematics of the planar mechanism is solved, and the Jacobian matrix is derived in this paper. Further, the singularity and the kinematic performance based on the kinematic equations are investigated, and the workspace of the mechanism is verified. Finally, a prototype was built to test the function of the proposed RCM mechanism. The results show that the mechanism can fulfill the constraint of MIS, and it can be used as the basic element of the active manipulator in an MIS robot.