This paper presents a novel underactuated coupled adaptive hand exoskeleton, called UCAS-Hand, which is designed to assist users with weak muscle strength to complete the operation of daily living items. In mechanical design, the proposed UCAS-Hand considers the human-robot kinematic compatibility, grasping adaptability for different objects, portability with motors attached to the hand, force transfer efficiency with applying normal force to the finger phalanges, and passive backdrivability with low gear reduction ratio motor. The UCAS-Hand can realize finger underactuated motions such as flexion/extension and thumb underactuated motions such as flexion/extension, abduction/adduction, and thumb opposability. To minimize the backlashes of bevel gear transmission, a spherical four-bar mechanism and a spherical seven-bar mechanism are designed for the index finger and thumb mechanisms, respectively. Finally, the experiment is implemented to reveal the characteristics of the UCAS-Hand.