It is important for a wearable robot to be compact and sufficiently light for use as an assistive device. Since human fingers are arranged in a row in dense space, the concept of traditional wearable robots using a rigid frame and a pin joint result in size and complexity problems. A structure without a conventional pin joint, called a jointless structure, has the potential to be used as a wearable robotic hand because the human skeleton and joint can replace the robot's conventional structure. Another way to reduce the weight of the system is to use under-actuation. Under-actuation enables adaptive grasping with less number of actuators for robotic hands. Differential mechanisms are widely used for multi-finger under-actuation; however, they require additional working space. We propose a design with a jointless structure and a novel under-actuation mechanism to reduce the size and weight of a hand exoskeleton. Using these concepts, we developed a prototype that weighs only 80 grams. To evaluate the prototype, fingertip force and blocked force are measured. Fingertip force is the force that can be applied by the finger of the hand exoskeleton on the object surface. The fingertip force is about 18 N when actuated by a tension force of 35 N from the motor. 18 N is sufficient for simple pinch motion in daily activities. Another factor related to performance of the under-actuation mechanism is blocked force, which is a force required to stop one finger while the other finger keeps on moving. It is measured to be 0.5 N, which is sufficiently small. With these experiments, the feasibility of the new hand exoskeleton has been shown.