A mass measurement system using relay feedback of velocity was developed. In this system, the velocity of the object was fed back through a relay with a hysteresis. Although the efficacy of the proposed method has been already confirmed experimentally, it was subject to drift mainly because only the velocity was fed back. To prevent such drift, a spring element was added to produce restoring force. However, smaller drifts still occurred and the trajectory of the object fluctuated because the switching positions are not determined uniquely. In this paper, an estimation formula is derived, which can estimate the mass regardless of switching positions. The efficacy of the derived formula is confirmed experimentally.