The growth structure of Fe on CU(001) was studied by scanning tunneling microscope. An analysis of size distribution of Fe islands on Cu(001) surface was made to determine whether Fe atoms mix with substrate Cu. The size distribution deviates from the standard scaling behavior, indicating that atomic density of Fe decreases with coverage up to 1 ML. The growth can be characterized by layer-by-layer scheme from 1 ML to 5 ML. This result agrees well with previously studied, Auger spectroscopy and RHEED result.