Based on the atomic force microscope observation of the three-dimensional mesostructure of Fe73.5Cu1Nb3Si13.5B9 alloy ribbon annealed at different temperatures, on the basis of experimental results of X-ray diffraction and the Mssbauer spectroscopy and theoretical results for this alloy ribbon, we systematically investigate the crystallization process of this alloy ribbon annealed at different temperatures, and propose a number of new concepts, such as the mesostructure with two-kinds of Nb-B framework, the agglomeration phase of the nanocrystalline grains, and the average numbers of nanocrystalline grains in unit volume. Finally, a hypothesis of the crystallization mechanism and the mesostructure model describing the crystallization process of this alloy are established. This model can be evolved to the two- or three-phase structure model.