The influence of AC current (with amplitud of Iac ＝0.2—20 mA and frequency of f＝1 kHz—1 MHz) upon the profile of gian magnetoimpedance (GMI) effect of a Fe-based nanocrystalline wire with transverse domain structure have been investigated. The experiment indicates that the GMI effect of the sample exhibits a two-peak feature. With the increasing of f, the peak field Hm increases, while Hm decreases even to H=0 when Iac increases. According to the current theoretical models, the peak field Hm should conrrespond to the transverse anisotropy field Hk, Hm=Hk. However, we found that this conclusion is correct only for the case of very small AC current. So a relationship Hm=Hk cos3θ, where θ is the angle between saturation magnetisation and the axis of wire, has been deduced by minimizing the energy in the process of magnetisation rotation. The experiments can be explained by this result.