To deliver more value to the healthcare industry, a specialized surgical robot is needed in the minimally invasive surgery (MIS) field. To fill this need, a compact hybrid robotic wrist with four degrees of freedom (DOFs) is developed for assisting physicians to perform MIS. The main body of the wrist is a 2DOF parallel mechanism with a remote center-of-motion (RCM), which is located outside the mechanism. From the mechanical point of view, it is different from existing 2DOF spherical mechanisms, since there is no physical constraint on the RCM. Other DOFs of the wrist are realized by a revolute joint and a prismatic joint, which are serially mounted on the movable platform of the parallel mechanism. The function of these DOFs is to realize the roll motion and the in-out translation of the surgical tool. Special attention is paid to the parallel RCM mechanism. The detailed design is provided and the kinematic equations are obtained in the paper. Further, the Jacobian matrix is derived based on the kinematic equations. Finally, the paper examines the singularity configurations and implements the condition number analysis to identify the kinematic performance of the mechanism.