Unbonded prestressed concrete (UBPC) has shown considerable promise for structural elements in continuous-use applications. However, little research has evaluated the performance of UBPC structural elements or their low energy absorption ability, and such elements are therefore not commonly used as main structural members. In this study, a small axially yielding hysteresis damper was developed, which can be replaced in the event of earthquake damage to a UBPC beam in high continuous use. The damper was designed to use the axial yielding of deformed rebars so that it has the same performance under compressive and tensile forces. It was mounted in a knee brace shape and had a mass of about 10 kg. The damper exhibited positive and negative hysteresis characteristics even after the deformed rebars had yielded axially and it had sufficient energy absorption capacity. In a structural experiment, installing the damper, the shear force that can be borne by the beam and the equivalent damping constant increased, which means that the damper is useful.