Hexagonal boron nitride (h-BN) has recently emerged as an excellent substrate for graphene nanodevices, owing to its atomically flat surface and its potential to engineer graphene's electronic structure. Thus far, graphene/h-BN heterostructures have been obtained only through a transfer process, which introduces structural uncertainties due to the random stacking between graphene and h-BN substrate. Here we report the epitaxial growth of single-domain graphene on h-BN by a plasma-assisted deposition method. Large-area graphene single crystals were successfully grown for the first time on h-BN with a fixed stacking orientation. A two-dimensional (2D) superlattice of trigonal moiré pattern was observed on graphene by atomic force microscopy. Extra sets of Dirac points are produced as a result of the trigonal superlattice potential and the quantum Hall effect is observed with the 2D-superlattice-related feature developed in the fan diagram of longitudinal and Hall resistance, and the Dirac fermion physics near the original Dirac point is unperturbed. The macroscopic epitaxial graphene is in principle limited only by the size of the h-BN substrate and our synthesis method is potentially applicable on other flat surfaces. Our growth approach could thus open new ways of graphene band engineering through epitaxy on different substrates.