Service robots are desired to be equipped with robot hands that are versatile to grasp various objects and are lightweight in consideration of robot mobility, power consumption and safety. In this paper, we propose a tendon-driven robotic finger with telescopic mechanism that can adjust its length for grasping objects of different sizes. Each phalanx is a nested structure and the telescopic mechanism is realized together with the bending mechanism using embedded wires and springs. Fingers can telescope up to 26.5% from its original length. Underactuated bending is designed to adapt to the shape of objects. A two-way pull-out test with a three-finger gripper to grasp seven sizes of cylindrical objects was carried out to evaluate the effectiveness of the telescopic finger. The results suggested that the change in finger length according to the objects can improve the gripping stability.