To ensure the anti-collapse capacity of the storey-adding out-jacketing frame cooperated with the existing structure,time-history analysis by IDARC(2D) on the out-jacketing frame under rear earthquake are carried out,which shows that the lateral stiffness of the frame is quite weak below the adding structure;the damages of the existing structure is more serious than the one of the adding structure;and some of the out-jacketing frame designed by Code for design of concrete structures(GB50010—2002) & Code for seismic design of buildings(GB50011—2002) collapse under rear earthquake.Based on the analysis,application limits,column axial compression ratio limits,end-column moment magnification factors and construction measure of the out-jacketing frame are presented.Time-history analysis shows that by these reinforcing measures,collapse of the out-jacketing frame can be prevented effectively.