The synthesis of lateral heterostructures assembled by atomically-thin materials with distinct intrinsic properties is important for future heterojunction-embedded two-dimensional (2D) devices. Here we report an etching-assisted chemical vapor deposition method to synthesize large-area continuous lateral graphene/hexagonal boron nitride (Gr/h-BN) heterostructures on carbon-containing copper foils. The h-BN film is first synthesized on the copper foil, followed by hydrogen etching, and then epitaxial graphene domains are grown to form continuous lateral heterostructures. Analyses, including Raman spectroscopy, atomic force microscopy, scanning electron microscopy, x-ray photoelectron spectroscopy, and ultraviolet-visible absorption spectroscopy, are used to characterize the coexistence of both materials and the highly continuous nature of this lateral heterostructure. This facile and scalable synthesizing method enables the potential usage of Gr/h-BN heterostructure in both fundamental studies and related 2D devices.