Vertical heterostructures of two-dimensional (2D) crystals have led to the observations of numerous exciting physical phenomena and presented the possibilities for technological applications, which strongly depend on the quality, interface, relative alignment, and interaction of the neighboring 2D crystals. The heterostructures or hybrids of graphene and superconductors offer a very interesting platform to study mesoscopic superconductivity and the interplay of the quantum Hall effect with superconductivity. However, so far the heterostructures of graphene and 2D superconductors are fabricated by stacking, and consequently suffer from random relative alignment, weak interfacial interaction, and unavoidable interface contaminants. Here we report the direct growth of high-quality graphene/2D superconductor (nonlayered ultrathin α-Mo2C crystal) vertical heterostructures with uniformly well-aligned lattice orientation and strong interface coupling by chemical vapor deposition. In the heterostructure, both graphene and 2D α-Mo2C crystal show no defect, and the graphene is strongly compressed. Different from the previously reported graphene/superconductor heterostructures or hybrids, the strong interface coupling leads to a phase diagram of superconducting transition with multiple voltage steps being observed in the transition regime. Furthermore, we demonstrate the realization of highly transparent Josephson junction devices based on these strongly coupled high-quality heterostructures, in which a clear magnetic-field-induced Fraunhofer pattern of the critical supercurrent is observed.