In this paper, a modular underactuated multi-fingered robot hand is proposed. The robot hand can be freely configured with different number and configuration of modular fingers according to the work needs. Driving motion is achieved by the rigid structure of the screw and the connecting rod. A finger-connecting mechanism is designed on the palm of the robot hand to meet the needs of modular finger’s installation, drive, rotation, and sensor connections. The fingertips are made of hollow rubber to enhance the stability of grasping. Details about the design of the robot hand and analysis of the robot kinematics and grasping process are described. Last, a prototype is developed, and a grab test is carried out. Experimental results demonstrate that the structure of proposed modular robot hand is reasonable, which enables the adaptability and flexibility of the modular robot hand to meet the requirements of various grasping modes in practice.