Graphene (G) and atomic layers of hexagonal boron nitride (h-BN) are complementary two-dimensional materials, structurally very similar but with vastly different electronic properties. Recent studies indicate that h-BN atomic layers would be excellent dielectric layers to complement graphene electronics. Graphene on h-BN has been realized via peeling of layers from bulk material to create G/h-BN stacks. Considering that both these layers can be independently grown via chemical vapor deposition (CVD) of their precursors on metal substrates, it is feasible that these can be sequentially grown on substrates to create the G/h-BN stacked layers useful for applications. Here we demonstrate the direct CVD growth of h-BN on highly oriented pyrolytic graphite and on mechanically exfoliated graphene, as well as the large area growth of G/h-BN stacks, consisting of few layers of graphene and h-BN, via a two-step CVD process. The G/h-BN film is uniform and continuous and could be transferred onto different substrates for further characterization and device fabrication.