Multimode vibration control of a non-linear building with distributed multiple tuned vibration absorbers (d-MTVAs) is studied to assess its seismic vulnerability. A multi-story building is exposed to earthquakes such that the beams and columns are likely to undergo material non-linearity which could be controlled. The modal properties of the linear un-controlled and controlled benchmark buildings are used sequentially to identify the optimum locations for the d-MTVAs. The seismic performance improvement achieved by installing the d-MTVAs on the building is compared with single tuned vibration absorber (STVA), multiple tuned vibration absorbers installed at the topmost floor of the building (MTVAs.all@top), arbitrarily d-MTVAs (ad-MTVAs), as well as when no such controllers are used. The variations of the inter-story drift and residual inter-story drift under different earthquakes are calculated to assess the efficiency of using the STVA, MTVAs.all@top, ad-MTVAs and d-MTVAs. Fragility functions for drift ratio are obtained to examine the seismic vulnerability of the building without and with the control measures. It is concluded that the building generally remains within elastic range upon installation of the MTVAs.all@top, ad-MTVAs and d-MTVAs. In addition, the efficiency of the d-MTVAs is found superior only if they are placed as per the optimum placement criteria. Further, the efficiency of the ad-MTVAs is quite similar to the MTVAs.all@top, except for the response of the first few floors at top of the building.