This paper proposes a two-dimensional active mass damper which is controlled by a software servo system in order to reduce the vibration of tower structures caused by strong winds or earthquake. The purpose of the two-dimensional active mass damper is to control effectively the two-dimensional 1st vibration modes of the structure. In designing the software servo system, LQ control theory is applied. The results of experirental examination on the design show that although the 1st vibration modes are well controlled, a resonance peak at the 2nd mode increases as a resonance peak at the 1st mode is decreased and runs into spillover instability. It is also shown that the spillover instability can be prevented easily by a dynamic absorber attached at the maximum amplitude point on the 2nd vibration mode.