This study is aimed at investigating the dynamic performance of a composite building structure under seismic ground motions. The building structure is an official fire department building located in southern Taiwan. It is composed of a seven-story reinforced concrete (RC) and an eight-story steel reinforced concrete (SRC) frame. Both frames share a common basement and are separated by expansion joints from the first to the seventh floor. Recorded floor accelerations of the building structure under eight earthquakes occurring during the period from 2011 to 2013 were examined in this paper. It is found that both frames had similar floor acceleration amplifications in the longitudinal direction, while the SRC frame revealed larger response than the RC frame in the transverse direction. Almost invariant and similar fundamental periods under the eight earthquakes in both directions were obtained from their transfer functions. Furthermore, numerical time-history simulations were carried out for the building structure under the most intensive earthquake. It is realized that the seismic response of the composite building was dominated by the first translational mode in each horizontal direction. Higher modes did not significantly contribute to the structural response. The conventional Rayleigh damping model could be appropriately applied to the time-history simulations under bi-directional excitations. Approximate floor acceleration envelopes were obtained with a compound RC and SRC structural model by using the average damping ratios determined from the different structural arrays.