Two-dimensional transition metal dichalcogenides (TMDCs) such as molybdenum sulfide MoS2 and tungsten sulfide WSe2 have potential applications in electronics because they exhibit high on-off current ratios and distinctive electro-optical properties. Spatially connected TMDC lateral heterojunctions are key components for constructing monolayer p-n rectifying diodes, light-emitting diodes, photovoltaic devices, and bipolar junction transistors. However, such structures are not readily prepared via the layer-stacking techniques, and direct growth favors the thermodynamically preferred TMDC alloys. We report the two-step epitaxial growth of lateral WSe2-MoS2 heterojunction, where the edge of WSe2 induces the epitaxial MoS2 growth despite a large lattice mismatch. The epitaxial growth process offers a controllable method to obtain lateral heterojunction with an atomically sharp interface.