“Strong column–weak beam, strong joint–weak member” is a core concept for the seismic design of buildings. For existing reinforced concrete (RC) frame buildings that do not satisfy this concept, installing RC wing walls beside existing columns is a simple and effective method for strengthening both columns and joints to promote a beam-hinging mechanism. In this study, a numerical simulation method is used to analyze the seismic performance of weak-joint RC frames strengthened by additional wing walls considering the column axial force ratio and to determine whether to consider the secondary load as a variable. The results show that when the secondary load is not considered, i.e. existing columns do not bear a load during the strengthening process, the strength, stiffness and energy dissipation of the structure increase with increasing axial force ratio, but the ductility of the structure decreases. When the secondary load is considered, the strength and initial stiffness of the frame are the greatest when the column axial force ratio is 0.4. When the axial force ratio is less than 0.4, the secondary load has less influence on the strength, stiffness and energy consumption. When the axial force ratio is greater than 0.4, the secondary load has a significant impact on the seismic performance of the strengthened structure, and the strength, stiffness, energy consumption and ductility are significantly greater than those in the case in which the secondary load is not considered. Additionally, the larger the axial force ratio is, the more significant the difference is. It is revealed that in engineering seismic strengthening using the wing wall installation method, the influence of secondary load on seismic performance should not be ignored, especially when the axial force ratio is large.