Currently, the preparation of large-size and high-quality hexagonal boron nitride is still an urgent problem. In this study, we investigated the growth and diffusion of boron and nitrogen atoms on the sapphire/h-BN buffer layer by first-principles calculations based on density functional theory. The surface of the single buffer layer provides several metastable adsorption sites for free B and N atoms due to exothermic reaction. The adsorption sites at the ideal growth point for B atoms have the lowest adsorption energy, but the N atoms are easily trapped by the N atoms on the surface to form N–N bonds. With the increasing buffer layers, the adsorption process of free atoms on the surface changes from exothermic to endothermic. The diffusion rate of B atoms is much higher than that of the N atoms thus the B atoms play a major role in the formation of B–N bonds. The introduction of buffer layers can effectively shield the negative effect of sapphire on the formation of B–N bonds. This makes the crystal growth on the buffer layer tends to two-dimensional growth, beneficial to the uniform distribution of B and N atoms. These findings provide an effective reference for the h-BN growth.