Here we demonstrate the deposition of a high-k dielectric material on graphene using hexagonal boron nitride (h-BN) nanosheets as a buffer layer. The presence of an h-BN layer on top of the graphene facilitated the growth of high-quality Al2O3 by atomic layer deposition (ALD). Simulation results also support the experimental observations and provide an explanation for the suitability of h-BN as a buffer layer in terms of mixed ionic-covalent B-N bonding. Additionally, h-BN works as a protective shield to prevent graphene oxidation during ALD of Al2O3 for the fabrication of graphene-based devices. Finally, triboelectric nanogenerators (TNGs) based on both Al2O3/h-BN/graphene and Al2O3/graphene structures are demonstrated for further confirming the importance of h-BN for synthesizing high-quality Al2O3 on graphene. It was found that the Al2O3/h-BN/graphene-based TNG reveals meaningful electric power generation under a mechanical friction, while no significant electric power output from the Al2O3/graphene-based TNG is obtained, indicating high charge storage capacity of the dielectric Al2O3 layer on h-BN.