In a minimally invasive surgical (MIS) robot, the remote center of motion (RCM) mechanism is usually used to realize the constrained motion of the surgical instrument. In this paper, a novel design method for planar 2DOF RCM mechanisms is proposed based on closed-loop cable transmissions. The concept is to utilize several coupled cable transmissions to constrain a serial kinematic chain. Through the analysis and determination of the transmission ratios for these cable transmissions, a class of planar 2DOF RCM mechanisms without any active or passive translational joints is obtained, which provides large workspace and low collision risk for the MIS robots. One of the resulting mechanisms is designed in detail and kinematically analyzed. To evaluate the influence of the elastic cables, a new error model for the proposed RCM mechanism is established through the static analysis and cable deformation analysis. Utilizing this model, the cable-induced error distributions of the tip and the RCM point are obtained, which show that these errors are within a relatively small range. Furthermore, the prototype of the proposed mechanism is built, and the accuracy experiments are conducted.