In steel beam-columns subjected to repeated horizontal loading, cumulative damage such as local buckling and/ or crack occurs and progresses in general with the increase of the number of repetition cycle. It is necessary to establish a method of predicting and evaluating the cumulative damage for securing the aseismic safety of steel frames. This study shows that a critical axial force for convergence-axial displacement curve can be obtained by test and the curve is effective for predicting the cumulative damage and evaluating a performance under cyclic loading. A way of predicting the cumulative damage in case of applying a variable axial force is also presented in this study.