We report strongly enhanced perpendicular magnetic anisotropy (PMA) of Co films by graphene coating from both first-principles and experiments. Our calculations show that graphene can dramatically boost the surface anisotropy of Co films up to twice the value of its pristine counterpart and can extend the out-of-plane effective anisotropy up to unprecedented thickness of 25 Å. These findings are supported by our experiments on graphene coating on Co films grown on Ir substrate. Furthermore, we report layer-resolved and orbital-hybridization-resolved anisotropy analysis, which help understanding of the physical mechanisms of PMA and more practically can help design structures with giant PMA. As an example, we propose superexchange stabilized Co-graphene heterostructures with a robust constant effective PMA and linearly increasing interfacial anisotropy as a function of film thickness. These findings point toward possibilities to engineer graphene/ferromagnetic metal heterostructures with giant magnetic anisotropy more than 20-times larger compared to conventional multilayers, which constitutes a hallmark for future graphene and traditional spintronic technologies.