The primary motivation of this study is to develop a sensor-less, easily controlled, and passively adaptive robotic gripper. A back-drivable pneumatic underactuated robotic gripper (PURG), based on the pneumatic cylinder and underactuated finger mechanism, is presented to accomplish the above goals. A feedforward grasping force control method, based on the learned kinematics of the underactuated finger mechanism, is proposed to achieve sensor-less grasping force control. To enhance the grasping force control accuracy, a state-based actuating force modeling method is presented to compensate the hysteresis error which exists in the transmission mechanism. Actuating force control experiment is performed to validate the effectiveness of the state-based actuating pressure modeling method. Results reveal that compared with the non-state-based modeling method, the proposed state-based actuating force modeling method could reduce the modeling error and control error by about 37.0% and 77.2%, respectively. Results of grasping experiments further reveal that grasping force could be accurately controlled by the state-based feedforward control model in a sensor-less approach. Adaptive grasping experiments are performed to exhibit the effectiveness of the sensor-less grasping force control approach.