This paper proposed a design idea of a novel under-actuated finger mechanism, and analyzed its principle and designed the finger mechanism. The finger is designed based on a gear-rack mechanism, spring constraint and particular active middle-segment, which is passively adaptive in grasping objects. A new multi-fingered hand named as TH-3R Hand is designed based on the finger. TH-3R Hand has 5 fingers, 15 DOF. Its all fingers are similar. TH-3R Hand has many advantages: it is simple in structure, light in weight, easy in control and low in cost. TH-3R Hand can passively adapt different shapes and sizes of the grasped object. It can be mounted in humanoid robot hand to make the hand obtain more DOF with less actuators, and good grasping function of shape adaptation, decrease the requirement of control system.