The growth properties of Fe overlayers on a stepped Cu(1 1 1) surface with a 8 degrees miscut angle were investigated by the CO titration method, Auger electron spectroscopy (AES), and low energy electron diffraction (LEED). The growth properties of Fe films on the stepped surface are found to be significantly different depending on the deposition temperature. At low substrate temperatures (T-s < 200 K), the Fe films grow in a 2D island mode retaining the step periodicity of the stepped Cu(1 1 1) surface, while at room temperature, even the submonolayer of Fe deposition (theta = 0.3 ML (monolayer)) significantly alters the step structure of the substrate and the Fe films grow in a 3D island mode.