This study proposes a new design method for an active mass damper (AMD) that is based on auto-regressive exogenous models of a building structure. The proposed method uses the results of system identification in the field of active structural control. The uncontrolled structure is identified as auto-regressive exogenous models via measurements under earthquake excitation and forced vibration. These models are linked with an equation of motion for the AMD to introduce a state equation and output equation for the AMD-structure interaction system in the discrete-time space; the equations apply modern control theories to the AMD design. In the numerical applications of a 10-degree-of-freedom building structure, linear quadratic regulator control is used to understand the fundamental characteristics of the proposed design procedure. The feedback control law requires the AMD's acceleration, velocity and stroke; the structure's acceleration; and the ground acceleration as vibration measurements. The numerical examples confirm the high applicability and control effectiveness of the proposed method. One remarkable advantage of the proposed method is that an equation of motion for the structure becomes unnecessary for designing controllers. Copyright (C) 2016 John Wiley & Sons, Ltd.