Na3PS4 crystals with high ionic conductivity are promising solid-state electrolytes. Here, a novel phase of Na3PS4 (β'-NPS) crystallizing in a cubic lattice with a space group of P4̄3m was systematically investigated using first-principles calculations. First of all, β'-NPS is determined to be thermodynamically, dynamically and mechanically stable. The phase transition from tetragonal Na3PS4(α-NPS) to a cubic β'-NPS system occurs at approximately 480 K, suggesting high feasibility of experimental access. Moreover, the β'-NPS is an insulator with a large band gap of 4.05 eV and a low migration energy barrier of 0.10 eV for an interstitial Na ion. Significantly, a novel Na ion diffusion mechanism, that is, interstitial diffusion, is proposed, in contrast to traditional vacancy diffusion or kick-off diffusion as observed in most solid electrolytes. This work proposes β'-NPS as a promising superionic conductor for sodium ion batteries and provides theoretical guidance towards designing future ideal solid-state electrolytes.