In this article, we propose a novel shape memory alloy (SMA) strip-based bending actuator for a soft robotic hand. Soft robots have significant advantages of safety, adaptability, and dexterity compared with traditional rigid body robots. However, one challenge of soft robots is the design and modeling of effective actuators. This article presents a bending actuator using SMA strips. An analysis model and a design model of the SMA strip actuator are developed to predict output performances and provide guidance to designers. The experiments are conducted to verify the proposed models. We then apply this actuator to a soft robotic hand with five fingers. Experiments show that the pinch force of the soft robotic hand is *3 N, whereas the power grasping force is 9.7 N. The soft robotic hand is designed to be inherently safe to human operators because of its light weight (about 250 g), low stiffness, and its capability of sustaining large external impacts. The proposed actuator may also have other potential applications in biomimetic soft robots and prosthetic soft robots.