The first-principles approach based on density functional theory (DFT) and the full-potential linearized augmented plane-wave method were employed to investigate the structural, elastic, electronic and magnetic properties of Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys. The generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof (PBE) and the modified Becke–Johnson exchange potential were used. As far as we know, we present our results which for the first time quantitatively account for the electronic structures and magnetic properties of Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys. From the total energy calculation using three possible atomic configurations ([Formula: see text], [Formula: see text] and [Formula: see text]), it is found that the Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys are more stable in the ferromagnetic [Formula: see text]-phase. From our estimated elastic constants [Formula: see text], it is found that all the considered Heusler alloys are mechanically stable in the [Formula: see text]-phase. We have also investigated the robustness of the half-metallicity with respect to the variation of lattice constants in these alloys. We have found that these alloys are half-metallic ferromagnets (HMFs) with a magnetic moment of 2[Formula: see text][Formula: see text] per formula unit at their equilibrium volumes. The spin-polarized electronic band structure and density of states of these quaternary half-Heusler alloys calculated by GGA (mBJ-GGA) show that the minority spin channels have metallic nature and the majority spin channels have a semiconductor character with half-metallic gaps of 0.49[Formula: see text]eV (2.17[Formula: see text]eV), 0.72[Formula: see text]eV (2.28[Formula: see text]eV) and 0.96[Formula: see text]eV (2.22[Formula: see text]eV) for NaCaNO, NaSrNO and NaBaNO quaternary half-Heusler alloys, respectively. Analysis of the density of states and the spin charge density of these quaternary alloys indicates that their magnetic moments mainly originate from the strong spin-polarization of 2[Formula: see text] states of N atoms and O atoms.