The mesostructure in Fe-based (Fe73.5Cu1Nb3Si13.5B9) nanocrystalline ribbons annealed under different stress (FNRAS) was investigated by observation of the cross section images of the ribbons with atomic force microscopy (AFM) and X-ray diffraction. The longitudinally driven giant magneto-impedance and transversal magnetic anisotropy field (Hk) were measured. The mechanism of the transversal magnetic anisotropy field can be explained by the mesostructure of the directional preference of crystalline grain (coated with amorphous shell) gathering, along the transverse direction, induced in the course of annealing of the Fe-based alloy ribbons under stress.