Soft robots can accomplish hand rehabilitation training to ensure better safety and compliance for hand rehabilitation. In this study, a wavy nonrotating soft actuator structure was proposed for hand rehabilitation, and an axial stiffener was added to the main structure of the actuator according to the function of the bamboo fiber. A physical model of the actuator was fabricated using a multistep casting molding method, and the performance of the designed soft actuator was tested experimentally. The results showed that the bending angle and contact force gradually increased with increasing pressure. The average maximum bending angle and contact force can reach 286 ± 14.3 deg and 1.04 ± 0.051 N, with a pressure of 72 kPa. Meanwhile, the bending torques of the soft actuator at each joint of the finger were tested, to verify that it can meet the needs of soft actuators for hand applications. Furthermore, the load lifting of the soft actuator with axial stiffeners can increase by 6 mm on average compared with a soft actuator without axial stiffeners under negative pressure. In conclusion, the pneumatic soft actuator can produce two different motion functions under the action of one cavity. In addition, a soft actuator with an axial stiffener can improve the load capacity under negative pressure. By assembling the actuators, a three-finger gripper was manufactured. The gripper could grasp and lift objects. Therefore, this work provides a new route for the development of pneumatic soft actuators and soft robots, which has efficient driving.