Commercial multi-degrees-of-freedom (multi-DOF) myoelectric hand prostheses can perform various hand gestures and grip motions using multiple DOFs. However, as most upper limb amputees have less than two electromyogram (EMG) signals generated at the amputation site, it is difficult to control various hand gestures and grip motions using multi-DOF myoelectric hand prostheses. This paper proposes a multifunctional myoelectric hand prosthesis system that uses only two EMG sensors while improving the convenience of upper limb amputees in everyday life. The proposed system comprises a six-DOF myoelectric hand prosthesis and an easy and effective control algorithm that enables upper limb amputees to perform various hand gestures and grip motions. More specifically, the hand prosthesis has a multi-DOF five-finger mechanism and a small controller that can be mounted inside the hand, allowing it to perform various hand gestures and grip motions. The control algorithm facilitates four grip motions and four gesture motions using the adduction and abduction positions of the thumb, the flexion and extension state of the thumb, and three EMG signals (co-contraction, flexion, and extension) generated using the two EMG sensors. Experimental results indicate that the proposed system is a versatile, flexible, and effective hand prosthesis system for upper limb amputees.