<p>As cathode materials for alkali-ion batteries, sodium manganese oxides have been receiving considerable and continuous attention in recent decades. In this work, the structure and environment-dependent stability of NaMn₂O₄ surface were studied based on the first principles calculations. The surface stability diagram of NaMn₂O₄ involving various different terminations of (100), (110) and (111) surfaces was constructed, and the stability of these different terminations could be compared as a function of chemical environment. It is found that the (100)-MnO and (111)-ONa terminations are two more stable terminations under the investigated chemical conditions. And the surface energies of (110) surfaces are negative under the investigated chemical potential, hence, (110) surfaces are unstable. The surface energy of NaMn₂O₄ as a function of O chemical potential is also investigated under constant Na chemical potential. The structure relaxation indicates that the surface rumpling and surface reconstruction can affect the electronic structure of the surface, thereby reducing surface energy and stabilizing the surface. Furthermore, the Wulff shape of NaMn₂O₄ was also constructed based on Gibbs-Wulff theorem.</p>