Injecting carriers into single-crystal h-BN poses a challenge toward the development of h-BN-based high-power electronics and optoelectronics. Introducing C to create an h-BN/graphene hybrid material has been proposed as a potential method for ohmic current injection. This material resulted in ohmic conduction, which was initiated by the formation of a conductive path at high temperatures and voltages. Through comprehensive characterizations, C is the key component in this path. Our present results provide insight into the nature of this conductive path and the potential of hybrid material for future applications.