This paper introduces a new designed modular tactile sensing dexterous hand for domestic service robots. This fully-actuated hand consists of 1 palm and 3 fingers, with embedded tactile sensors, motors and control boards. The palm and each finger have 2 degrees of freedom (DOFs). The modular design makes it easy to attach and detach the hand, even by inexperienced users. The tactile sensor unit with new structure can help to decrease sensor number and keep a good sensing ability. A series of experiments to test the sensor unit and evaluated the hand performance with an object set was performed in this paper. The results show that the sensor unit can provide precise sensing result and perceive continuous vibration data, and the hand has excellent grasp ability. In addition to its good performance, the hand features a cost of $500 USD with a scale of one hundred sets. This hand is affordable for researchers and for domestic service robots in the consumer market. In future research, this hand will be used to promote the robotic manipulation research based on visual and tactile data.