Linear motors are promising actuators for active mass dampers, because driving mechanisms using them become more simple, reliable and efficient than those of current mass dampers which use AC servomotors and hydraulic actuators. Control methods using directly measured absolute accelerations of the buildings as feedback signals, are expected to he more reliable than those of current mass dampers using relative velocities and displacements to the ground which are calculated from the absolute accelerations. In this study, controllers were designed for the acceleration feedback control for a mass damper using a linear motor, based on the H^∞ control theory and a model-matching method. A gain-scheduled control law was also developed for the acceleration feedback control. Excitations tests were carried out for a 5-story building model of a 5 800 kg total mass and a 3.4 m height with a mass damper model on the roof. Through the tests, it was shown that the H^∞ controllers had higher performance than the model-matching controllers, and the gain-scheduled control law was very effective.