Retrofit of soft-story buildings due to seismic loads using Gap-Inclined-Brace (GIB) system is considered a new retrofit technique that aims to maintain both strength and stiffness of structure. In addition, it provides more ductility and less P delta effect, and subsequently better performance is observed. In this paper, the effect of the eccentricity between GIB and the retrofitted column due to installation on the efficiency of the retrofitting system is studied. In addition, a modification in the determination method of GIB properties is introduced to reduce the eccentricity effect. Also, the effect of GIB system on the seismic response of mid-rise buildings with different heights considering soft-story at various heights has been studied. A numerical model is developed to study the impact of such system on the response of retrofitted soft-story buildings under the action of seismic loads. To achieve that goal, this model is used to perform a numerical investigation, by considering five case study scenarios represent several locations of soft-story of two mid-rise reinforced concrete buildings. At first, Non-linear static pushover analysis was carried out to develop the capacity curves for case studies. Then, Non-linear time history analyses using ten earthquake records with five peak ground accelerations is performed for each case study scenario before and after retrofitting with GIB. The results show that large GIB eccentricity reduce the ultimate lateral resistance and deformation capacity of the retrofitting system. Moreover, the higher the retrofitted building, the more deformation capacity is observed but without significant increase in ultimate lateral resistance.