In this paper, a unified averaged modeling method is proposed to investigate the fast-scale period-doubling bifurcation of a full-bridge integrated buck-boost inverter with peak current control. In order to increase the resolution of the conventional classic averaged model to half the switching frequency, sample-and-hold effect of inductor current is absorbed into the averaged model, i.e. the proposed unified averaged model can capture the high-frequency dynamical characteristics of the buck-boost inverter, which is both an extension and a modification of conventional averaged model. Based on the unified mode, fast-scale bifurcation is identified, and the corresponding bifurcation point is predicted with the help of the locus movement of all the poles, and their underlying mechanisms are revealed. Detailed analysis shows that the occurrence of high-frequency oscillation means fast-scale bifurcation, while the occurrence of low-frequency oscillation leads to slow-scale bifurcation. Finally, it is demonstrated that the unified averaged model can provide not only a general method to investigate both the slow-and fast-scale bifurcations in a unified framework but also a quite straightforward design-oriented method which can be directly applicable.