Local buckling refers to a failure pattern of a structural steel member. It is characterized by lower ability to withstand compressive stress than the stress that the steel material is designed to withstand. This paper highlights the effects of local buckling on the structural behavior of steel columns subjected to elevated temperatures with the aim of developing a suitable design method for the local buckling of the high-strength Q690 steel column at elevated temperatures. The local buckling of high-strength Q690 steel columns is numerically investigated by FE modeling using software ABAQUS. The developed FE models are validated against the experimental results of local buckling for high-strength Q460 steel columns under axial compression previously conducted by other researchers. Subsequently, a parametric study was carried out to evaluate the influence of several parameters affecting the design of steel members to resist local buckling such as the width-to-thickness ratio, temperature, initial imperfection, residual stress and interaction between the flange and web of the H-shaped cross-section. The results showed that local buckling is significantly affected by the width-to-thickness ratio; increasing the width-to-thickness ratio led to a reduction in the ultimate bearing capacity of the specimens. It also indicated that both initial imperfections and residual stress have a significant effect on local buckling stress. Furthermore, it was observed that the overall capacity of the specimens deteriorates significantly as the temperature increases. Based on the results, a simplified design method and new width-to-thickness ratio limits were proposed for the H-shaped high-strength Q690 steel compression members. The results data were also compared with the design rules provided by GB 50017-2017, Eurocode 3, and ANSI/AISC 360-10.