While the integration of graphene on semiconductor surfaces is important to develop new applications, epitaxial graphene has only been integrated on SiC substrates or 3C-SiC/Si templates. In this work, we explore the possibility of growing graphene on AlN/Si(111) templates. Using a chemical vapor deposition process with propane as the carbon source, we have obtained graphitic films (from 2 to 10 graphene layers) on AlN/Si(111) while preserving the morphology of the AlN layer beneath the graphitic film. This study is an important step for the integration of graphene with semiconductors other than SiC.