Prosthetic hand is an artificial device which replaces the missing hand of an amputee. In this research, a multi-functional prosthetic hand with self-adaptation ability is proposed. The prosthetic hand enables user to grasp different objects by performing cylindrical grasp, hook grasp, lateral pinch and tip pinch and palmar pinch. Finger mechanism of the proposed prosthesis is capable of generating passively different flexion/extension angles for a proximal interphalangeal (PIP) joint and a distal interphalangeal (DIP) joint for each flexion angle of metacarpophalangeal (MCP) joint. In addition, DIP joint is capable of generating passively different angles for the same angle of PIP joint. The design includes thumb opposition/apposition in addition to its flexion/extension. Finger has an under-actuation mechanism using one actuator to drive all proximal, middle and distal phalanxes. Kinematic analysis of the finger has been carried out to verify the required range of motions of the joints. Simulations and experiments verify the effectiveness of the proposed hand prosthesis.