This paper applies the dynamic model reduction method to obtain a reduced order model of an experimental tall building which has twenty floors and is 2.5m high. The experimental model is designed to imitate a real tall building with an active mass damper, and is used to study the available modelling and active control strategies for real tall buildings. Based on the dynamic model reduction method, a reduced order model is used within a Hinfin controller design to suppress excessive vibrations induced by seismic excitation. The reduced order model effectively describes only those frequency characteristics from the full order model that are of interest. The controller design based on the low order model can be directly applied to the full order model without introducing the control and observer spillover problems. Numerical simulations confirm that the low order model is acceptable at describing the relevant dynamic characteristics of the full order model and that it can be used effectively to mitigate the vibration caused by seismic disturbances.