With its atomically smooth surface yet no dangling bond, chemical inertness and high temperature sustainability, the insulating hexagonal boron nitride (h-BN) can be an ideal substrate for two-dimensional (2D) material growth and device measurement. In this review, research progress on the chemical growth of 2D materials on h-BN has been summarized, such as chemical vapor deposition and molecular beam epitaxy of graphene and various transition metal dichalcogenides. Further, stacking of the as-grown 2D materials relative to h-BN, thermal expansion matching between the deposited materials and h-BN, electrical property of 2D materials on h-BN have been discussed in detail.