Past earthquake disasters have shown that irregular gravity load designed (GLD) reinforced concrete (RC) frame buildings were very vulnerable to strong ground shaking. Many of them collapsed and caused loss of human lives as well as materials. Hence, in order to prevent future disasters, this type of buildings needs to be strengthened against earthquake. This paper presents a case study of an innovative approach for seismic strengthening of a typical six story residential building with a soft/weak first story using buckling restrained braces (BRBs). The seismic performance of the original GLD building and the retrofitted one are compared using three dimensional nonlinear dynamic time history analysis in OpenSees. The analysis results show that the innovative seismic strengthening approach for irregular GLD RC frame buildings using BRBs can significantly reduce maximum story drifts as well as building damages which benefits in reducing the risk of building?s collapse during earthquake.