The initial stage of the growth process of Fe submonolayer films on a vicinal Au(001) surface was studied by means of a scanning tunneling microscope. The vicinal Au(001) surface was characterized by an average terrace width of 20 nm, separated by straight, monoatomic steps aligned along the [110] or [110] direction. The correlation between the formation of steps and the reconstructed structure is discussed. One-dimension-like Fe structures with 4 nm width and 0.5 nm height have been grown by decoration of monoatomic steps of Au(100) surface.