In recent decades, the considerable number of worldwide earthquakes caused considerable damage and several building collapses, underlining the high vulnerability of the existing buildings designed without seismic provisions. In this regard, this work analyses the seismic performance of a reinforced concrete building designed without any seismic criteria, characterized by a seismically-stronger and a seismically-weaker direction, such as several existing reinforced concrete-framed structures designed for vertical load only. The case study building was modelled in OpenSees considering a non-linear three-dimensional model, also accounting for the contribution of joint panel deformability on the global behavior. Thirty bidirectional ground motions have been applied to the structure with the highest component alternatively directed along the two principal building directions. Time-history analyses have been performed for eight increasing hazard levels with the aim of evaluating the influence of bidirectional ground motion on structural response and estimating the seismic vulnerability of the building. The seismic performance of the structures are provided in terms of fragility curves for the two principal directions of the building and for different damage states defined according to the European Macroseismic Scale.