Soft robotic hand/gloves for hand rehabilitation can aid the performance of activities of daily living (ADL). Although existing soft robotic hands can assist with finger flexion, few have addressed finger extension, which is a challenging task for stroke patients due to poststroke spasticity. In this article, we describe the design of a composite actuator, the soft-elastic composite actuator (SECA), to facilitate both finger flexion and extension. A double-segmented SECA comprising two serially connected fiber-reinforced actuators with two bottom torque-compensating layers was fabricated. The SECA bends and extends by pneumatic actuation, and the torque-compensating layers offer an assistive bending moment to configure the bending moment inside the SECA. The principles associated with selection of the torque-compensating layer are described. Analytical models were established to quantify the input pressure and the bending angle of SECA with free bending and when placed on a model compromised hand. The analytical models were validated experimentally and by the finite element method. Moreover, a stroke survivor was recruited to test the new robotic glove integrated with the multiple double-segmented SECA. The robotic glove facilitated hand opening and closing by the patient, and successfully assisted with grasp of a Chinese chess piece and twisting of a towel.