We carry out photoluminescence (PL) study on Na-doped ZnO nanorods to provide insights into the behavior of Na acceptor. We demonstrate the successful growth of Na-doped ZnO nanorods array by metalorganic chemical vapor deposition. PL analysis reveals the very low concentration of deep level defects such as oxygen vacancy. Unlike most ZnO materials, the low temperature PL of Na-doped ZnO nanorods is dominated by excitons bound to ionized donors (D+X), suggesting the formation of Na acceptors and high compensation between the donors and acceptors. The formation of Na acceptors is supported by the shift of Fermi level toward the valence band.