Stacked structures of graphene/hexagonal boron nitride (G/h-BN) exhibit high carrier mobility, thermal stability, and deep ultraviolet absorption properties which are considered important for developing various novel devices. However, the realization of their large-scale fabrication and the improvement of performance are technically limited by the complicated exfoliation and transfer processes during fabrication. In this study, the h-BN film was successfully deposited by RF-magnetron sputtering and was used as an alternative to metal catalysts in the synthesis of graphene via low pressure chemical vapour deposition. This provides an alternative strategy to avoid any exfoliation and transfer processes in the development of G/h-BN stacked structures. The stacked structure was confirmed by Raman spectroscopy, atomic force microscopy, and x-ray photoelectron spectroscopy. The stacked films were found to be uniform, continuous and well doped with boron and nitrogen. The fabrication parameters were optimized to obtain high-quality graphene, and the formation mechanism of graphene on the BN film was also investigated.