The seismic Vulnerability of unsymmetrical reinforced concrete (RC) frame buildings has become the subject of significant interest in recent years because of their associated geometrical complexities, asymmetrical mass and stiffness distribution, torsional effects and vulnerability to structural damage during earthquakes. The R factor is an important parameter in the seismic design of the structure. The R factor represents the ability of the building to withstand lateral forces. However, its impact on the seismic vulnerability of unsymmetrical RC frame buildings has yet to be researched extensively. This study considers an L-shaped RCC frame building, which is modeled in SAP2000. Pushover analysis has been carried out to understand the nonlinear behavior of the building for various R factors. The base shear capacity and demand ductility have been estimated for different R factor values. Finally, the results are presented as fragility curves and the probability of damage at various earthquake intensities, such as DBE and MCElevels, for different R factors. It is observed that an increase in the R factor value reduces the base shear capacity but increases the damage probabilities in various damage states. The results of this study will help to understand how unsymmetrical RC frame structures respond to earthquakes and how the R factor affects their Vulnerability. The effect of the R factor on unsymmetrical RC frame buildings may assist in updating building codes and guidelines. The findings will be helpful for the engineers, architects, and legislators connected with the seismic design and assessment of unsymmetrical structures.