InN epitaxial growth on a (111)-oriented, Ga-doped germanium substrate using molecular beam epitaxy is described. X-ray diffraction and transmission electron microscopy investigations have shown that the InN epitaxial layer consists of a wurtzite structure, which has the epitaxial relationship of (0001) InN ∥(111) Ge . Transmission electron microscopy shows an intermediate layer at the interface between the InN/Ge substrate. Consistent with recent reports implying a narrow bandgap of InN [Phys. Stat Sol. B 229 (2002) R1, Appl. Phys. Lett. 80 (2002) 3967], a strong photoluminescence with peak energy of 0.69eV at 15K was observed for this InN epilayer, in contrast to the peak energy of 0.71eV for Ga-doped Ge under the same measurement conditions.