Restoring human grasp functions by prosthesis is a long-standing challenge in robotics research. Aiming at prosthetic applications, this paper presents a novel anthropomorphic multi-grasp hand design. The hand is driven by only one motor, and several mechanisms were designed for enhanced functionality. First, a continuum differential mechanism (CDM) was used to generate differential finger motions and to simplify the transmission of the hand. Second, a load adaptive variable transmission (LAVT) was designed to magnify the grasp forces. Moreover, a prismatic clutch is embedded in the hand, to lower the motor's energy consumption. Myoelectric control was implemented using affordable control hardware and sensors. All the above components are integrated in the proposed prosthetic hand, which is an average adult male size and weighs 470 g (including batteries). Experiments, including a preliminary clinical evaluation, were conducted to assess the effectiveness of the hand for prosthetic use. The results show that the hand can perform various grasps and can be a viable option for transradial prosthesis.