The morphology of BN seeds can be experimentally controlled and has a certain influence on the structural quality and nucleation efficiency of the surrounding graphene. By adopting the calculations using the density functional theory combine with transition state, we found that the sharp corners of normal triangular BN seed hinder the continuous C adsorption and aggregation around BN, and they can be etched by H2. Therefore, we theoretically investigated the process of etching triangular BN seeds with H2, along with the influence of BN seed morphology on the nucleation and growth of graphene on Cu substrates. The etching sequence of BN occurs from the corner N atom to the corner B atom, and the atoms at the side edge are inactive due to their higher adsorption energies and reaction barriers. After etching the BN seeds from a triangular to a hexagonal morphology, the graphene nucleation rates are up to ten times higher than those before etching and 105 times higher than those on a perfect Cu substrate. These results suggest the possibility of fabricating desirable BN edge structures and morphologies, and also provide a convenient way to improve the quality and growth rate of graphene on the Cu substrate.