In this paper, the dynamical responses and control performance of a building structure with a delayed track nonlinear vibration absorber are studied. The amplitudefrequency response curves of the system under external excitation are given by harmonic balance method and arclength continuation method. The fourthorder Rungekutta algorithm is performed to validate the obtained results. The properties of the amplitudefrequency response for different system parameters are analyzed and complex dynamical motions are shown. It is shown that the track nonlinearity can lead to the leftleaning phenomenon. In addition, the delayed feedback control can reduce the displacement amplitude of the primary structure and suppress the complicated responses.