Abstract: Based on QR method, the stability of a steel semi-rigid frame was studied in this paper. A general semi-rigid beam element model with a zero-length rotational spring at both ends of the beam was used. The mechanical properties of semi-rigid connections were simulated by a rotational spring and a Kish-Chen three-parameter model. Considered the second-order effect, adopted a plastic hinge model and a modified Newton-Raphson iteration method, the calculation format and steps of QR method for the second-order elastic-plastic stability analysis of steel frames were constituted. Furthermore, the corresponding C++ source codes were designed. Finally, the stability of a typical steel frame was analyzed. The superiority of this method was showed.