Because of the rapid aging of the Japanese population and the acute decrease in young workers in Japan, robots are anticipated for use in performing rehabilitation and daily domestic tasks for nursing and welfare services. Use in environments with humans, safety, and human affinity are particularly important robot hand characteristics. Such robot hands must have flexible movements and be lightweight. Under these circumstances, this study specifically addresses the expansion of a silicone rubber, tendon-driven actuator, which has been developed using a pneumatic balloon. A multifingered robotic hand using the actuator is developed. Moreover, a fuzzy grasping control system is applied to the proposed robotic hand. The robot hand’s development is described incorporating pneumatic balloon actuator with the softness, size, and weight of a human hand. The fuzzy grasping control system is shown to be effective for the proposed robot hand, which can grasp soft objects easily.