The first-order plastic hinge method (FPHM) is simple in theory and efficient in calculation because it can rapidly estimate the position of plastic hinges and the ultimate strength of steel frames according to the proportionality property between the external load and the linear elastic bending moment. However, it ignores the combined action of axial force and bending moment on the development of plastic hinge. The refined plastic hinge method (RPHM) overcomes the limitation of the FPHM, but it determines the position of plastic hinges and the ultimate strength of the structure only by incremental adjustment of external load and iterative trial calculation, which results in the loss of proportionality property and makes the formulation complex and the computation efficiency low. The generalized plastic hinge method (GPHM) possesses the advantages of both the FPHM and the RPHM but ignores the effect of the residual stress, which leads to the overestimating of the ultimate strength of frames with columns objected to large vertical concentrated loads. To solve these problems, this paper introduces the stability coefficient to modify the initial axial strength of the section under the generalized yield criterion, and then an improved GPHM is established to rapidly evaluate the ultimate strength of steel frames with the consideration of the influence of residual stress. In the investigation, firstly, each loading step’s modified section strength is established using the strength reduction factor. Next, the homogeneous generalized yield function is established through regression analysis and the element bearing ratio, which maintains the same proportional relationship with the external load, is defined. Then, the stability coefficient is introduced to modify the initial axial strength of the section to consider the influence of residual stress. Finally, according to the proportional relationship between the element bearing ratio and the external load, the position of the plastic hinge and the corresponding load increment in each loading step are determined. By comparing and analyzing several calibration examples in literatures with different methods, it is found that the computational efficiency of the proposed method is approximately 3~12 times that of the current general structural analysis method.