Graphene nanostructures with defined edges are proposed as a promising platform for the realization of nano-electronics and spin-electronics. However, patterned graphene nanostructure can lead to extra damage and drastically reduce its charge carrier mobility due to the edge disorder. The high flexibility of a top-down patterning method with edge smoothness is extremely desirable. Hydrogen plasma enhanced anisotropic etching graphene is demonstrated to be an efficient method of fabricating zigzag-edge graphene nanostructures. In addition, boron nitride is shown to be an excellent substrate for graphene due to its atomic flatness. Here in this work, we fabricate zigzag edge graphene antidot lattices on a boron nitride substrate via dry transfer method and traditional electron beam lithography, and reactive ion etching followed by hydrogen anisotropic etching approach. At low magnetic fields, weak localization is observed and its visibility is enhanced by intervalley scattering on antidot edges. We observe commensurate features in magnetotransport properties which stem from carriers around one antidot, signifying the high quality of our patterned samples. At high magnetic field, crossover from Shubnikov-de Haas oscillation to quantum Hall effect can be clearly observed due to the high mobility of our zigzag edge graphene antidot lattices. The transport properties of our patterned samples suggest that our fabrication method paves the way for achieving high quality graphene antidot lattices. High quality zigzag edge graphene antidot lattice might be a great platform to study the transport properties of lateral superlattice potential modulation graphene.