The adsorption behavior and stable geometries of ferrocene molecule on pristine, oxygen and hydroxyl functionalized graphene surfaces are investigated by using first principle density functional calculations based on the PBE-D2 method, which uses GGA-PBE functional with the incorporation of van der Waals (VDW) forces. Our calculations reveal that on all graphene substrates (pristine, oxygen and hydroxyl functionalized), the ferrocene molecule adsorbed with its molecular axis parallel to the surface. Oxygen and hydroxyl functionalized graphene systems have higher adsorption energies, higher charge transfer values and shorter adsorption heights as compared to the pristine graphene. It is concluded that sandwich type pi-pi interaction along with the van der Waals forces plays a major role in these adsorptions. The physisorption of ferrocene molecule is supported by the optimized geometrical parameters, adsorption energies and electronic properties. As the activity of a catalyst relies on the controlled adsorption of molecules onto surfaces, we therefore anticipate that these calculations can play an important role in the investigation of catalytic behavior of a catalyst based on the combined systems of graphene and ferrocene molecule. These findings offer more detail investigation of the ferrocene molecule/ molecules on different types of graphene surfaces, and we hope that these calculations can open a new way for the upcoming work on other molecules of the metallocene family.