Initial stage of Fe growth on Cu(001) surface has been studied using scanning tunneling microscopy. Growth can be characterized predominantly by a layer-by-layer scheme up to 5 ML, The island size distributions are scaled to different curves at the submonolayer regime, suggesting atomic mixing at the first layer. Interdiffusion may occur through the atomic defects or impurities on the Cu surface, Annealing the grown Fe film results in change of the surface morphology.