The work proposes an underactuated design of a glove-like soft hand exoskeleton for grasping and lifting objects of varied shapes and sizes. Strings are used to flex all finger joints, assuming that finger anatomy of an impaired hand is intact. A pulley-based differential mechanism is designed to actuate all four fingers via a single motor to allow adaptive grasping. Two DC motors are used, one for flexion of all four fingers and the second for thumb flexion. Finger extension is passively achieved via elastic bands on the dorsal side. A prototype of the hand exoskeleton, weighing 300 g without battery is fabricated that occupies  mm space over the palmer side of the forearm. Novelty in the design lies in reducing the required length of the existing pulley-based differential mechanism from 20 cm to 10 cm. Lightweight, and compactness make the device portable. Performance of the soft exoskeleton is demonstrated via testing it on a healthy subject.