To grow precisely aligned graphene on h-BN without metal catalyst is extremely important, which allows for intriguing physical properties and devices of graphene/h-BN hetero-structure to be studied in a controllable manner. In this report, such hetero-structures were fabricated and investigated by atomic resolution scanning probe microscopy. Moiré patterns are observed and the sensitivity of moiré interferometry proves that the graphene grains can align precisely with the underlying h-BN lattice within an error of less than 0.05°. The occurrence of moiré pattern clearly indicates that the graphene locks into h-BN via van der Waals epitaxy with its interfacial stress greatly released. It is worthy to note that the edges of the graphene grains are primarily oriented along the armchair direction. The field effect mobility in such graphene flakes exceeds 20,000 cm(2)·V(-1)·s(-1) at ambient condition. This work opens the door of atomic engineering of graphene on h-BN, and sheds light on fundamental research as well as electronic applications based on graphene/h-BN hetero-structure.