The oxidation of ethylene (C2H4) to produce value-added chemicals such as ethylene oxide is an important chemical process in industry. We investigated the oxidation of C2H4 by O2 catalyzed by an Ag-atom embedded boron-nitride nanosheet (Ag/h-BN) using density functional theory calculations. The adsorption energies of O2 and C2H4 molecules on Ag/h-BN are -0.85 and -1.21 eV, respectively, demonstrating that C2H4 has a stronger tendency to interact with this surface. A trimolecular Langmuir-Hinshelwood mechanism involving the -CH2CH2OOCH2CH2- intermediate was found as the most efficient pathway for C2H4 epoxidation. This intermediate is converted into two ethylene oxide molecules after passing over an activation barrier of 0.44 eV. The competing pathway to produce an acetaldehyde molecule has a very high activation barrier, indicating that C2H4 epoxidation can occur selectively over Ag/h-BN. These findings may be useful for modeling and designing high performance and selective single-metal catalysts for ethylene epoxidation.