A numerical simulation of adaptive feedforward control of building structures under seismic inputs is presented. The control actuator is an active tuned mass damper (ATMD) located on the last floor of an eight-story shear type building. The properties of the tuned mass damper (TMD) are selected for optimum performance as a passive device, i.e. the natural frequency of the device is nearly the same as the fundamental frequency of the building. The feedforward compensator is implemented with a finite impulse response (FIR) filter. The ground acceleration is sensed and fed forward into the compensator to generate the control input. The adaptive algorithm updates in “real time” the compensator’s weights such that a critical response, referred as the error signal, is minimized. The relative displacement of the first floor, which is monitored with an error transducer, is the error signal to be minimized. The ground motion used for the computer simulation includes various real accelerograms. The passive TMD is able to attenuate the peak and root mean square (rms) responses by an average of 14.6 and 16.6%, respectively. The attenuation achieved for the hybrid passive/active control approach was 44.4 and 51.2%, respectively, which clearly demonstrates that the adaptive controller improves the effectiveness of the passive TMD to attenuate both the maximum and root-mean-square responses. The numerical simulation also shows that the algorithm adapts in “real time” for uncertainties and modeling errors in the system.