Vertical and lateral heterogeneous structures of two-dimensional (2D) materials have paved the way for pioneering studies on the physics and applications of 2D materials. A hybridized hexagonal boron nitride (h-BN) and graphene lateral structure, a heterogeneous 2D structure, has been fabricated on single-crystal metals or metal foils by chemical vapor deposition (CVD). However, once fabricated on metals, the h-BN/graphene lateral structures require an additional transfer process for device applications, as reported for CVD graphene grown on metal foils. Here, we demonstrate that a single-crystal h-BN/graphene lateral structure can be epitaxially grown on a wide-gap semiconductor, SiC(0001). First, a single-crystal h-BN layer with the same orientation as bulk SiC was grown on a Si-terminated SiC substrate at 850 oC using borazine molecules. Second, when heated above 1150 oC in vacuum, the h-BN layer was partially removed and, subsequently, replaced with graphene domains. Interestingly, these graphene domains possess the same orientation as the h-BN layer, resulting in a single-crystal h-BN/graphene lateral structure on a whole sample area. For temperatures above 1600 oC, the single-crystal h-BN layer was completely replaced by the single-crystal graphene layer. The crystalline structure, electronic band structure, and atomic structure of the h-BN/graphene lateral structure were studied by using low energy electron diffraction, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, respectively. The h-BN/graphene lateral structure fabricated on a wide-gap semiconductor substrate can be directly applied to devices without a further transfer process, as reported for epitaxial graphene on a SiC substrate.