Securing a semiconducting bandgap is essential for applying graphene layers in switching devices. Theoretical studies have suggested a created bulk bandgap in a graphene layer by introducing an asymmetry between the A and B sub-lattice sites. A recent transport measurement demonstrated the presence of a bandgap in a graphene layer where the asymmetry was introduced by placing a graphene layer on a hexagonal boron nitride (h-BN) substrate. Similar bandgap has been observed in graphene layers on metal substrates by local probe measurements; however, this phenomenon has not been observed in graphene layers on a near-insulating substrate. Here, we present bulk bandgap-like features in a graphene layer epitaxially grown on an h-BN substrate using scanning tunneling spectroscopy. We observed edge states at zigzag edges, edge resonances at armchair edges, and bandgap-like features in the bulk.