Teleoperation can assist humans in completing various complex tasks in inaccessible or high-risk environments. Adequate adaptability should be available to enable the exoskeleton master hand to capture the motion of human fingers and reproduce the contacting force between the slave hand and its object. This paper presents a novel finger exoskeleton based on the cascading four-link closed-loop kinematic chain. Each finger has an independent kinematic chain, and the angle sensor is employed to measure the finger movement including the flexion/extension and the adduction/abduction angle. The servo motor controls the tension of the tendon to transmit the contacting force to the fingers in real-time. An adaptive hand exoskeleton is consequently developed based on the finger exoskeleton. The experiment results show that the adaptive hand exoskeleton could be worn without any mechanical constraints, and the slave hand could follow the motions of each human finger. The accuracy and the real-time capability of the contacting force reproduction were validated to be superior. The designed adaptive hand exoskeleton could be employed as the master hand to remotely control the humanoid five-fingered dexterous slave hand, thus, enabling the teleoperation system to complete complex dexterous manipulation tasks.