This study proposes bi-directional coupled tuned mass dampers(BiCTMDs) for the seismic response control of two-way asymmetric-plan buildings when subjected to bi-directional ground motions. The proposed BiCTMD was developed from the three-degree-of-freedom(3DOF) modal system, which represents the vibration mode of a two-way asymmetric-plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two-way asymmetric-plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. This confirms that the BiCTMD is an effective approach for the seismic response control of elastic two-way asymmetric-plan buildings.