In this letter, we introduce an anthropomorphic robot hand by proposing a pneumatic dual-mode actuation mechanism powered by a compact pneumatic power generator based on the decomposition of hydrogen peroxide. Since the pneumatic power generator has limited gas supply ability for each fuel charge, a pneumatic dual-mode actuation mechanism is proposed to reduce the amount of gas consumed for each grasp action while maintaining the robot hand's fast grasping speed and large grasping force. Driven by the proposed pneumatic dual-mode actuation mechanism, the designed robot finger provides maximum 468 degrees/s flexion speed and 29.1 N fingertip force. Based on the proposed pneumatic dual-mode actuation mechanism, a robot hand with 198 x 79 x 31 mm(3) size and 420 g weight is designed. A differential mechanism and passive thumb abduction-adduction mechanism are applied for compact design and efficient gas consumption and the performance is verified with experiments. Finally, the robot hand was connected to the pneumatic power generator loaded with 80 ml of 70% hydrogen peroxide solution and provided more than 1250 repetitions of the grasping motion for the maximum gas consumption case, which is suitable to perform daily work when applied as a prosthetic hand.