Li4GeS4-substituted Li3PS4 crystals have high Li+ ion conductivities comparable to that of commercial organic electrolytes [Kamaya et al., Nat. Mater. 10 (2011) 682]. In this study, (100 - x)Na3PS4.xNa(4)GeS(4) glasses and glass-ceramics were prepared for novel Na+ ion conductors. These glasses, which have the highest Na content reported to date in the Na-P-Ge-S system, were prepared by a mechanical milling technique. These glasses are composed of PS43- and GeS44-. The crystallization temperatures gradually increased with increasing Na4GeS4 content. The glasses showed higher conductivities of similar to 10(-5) S cm(-1) than the Na-P-Ge-S glasses reported so far. The glass-ceramics with the compositions x = 50 and 75, where the crystal predicted by first principles calculations to have high conductivities exceeding 10(-3) S cm(-1) was precipitated, exhibited Na+ ion conductivities of similar to 10(-5) S cm(-1) at room temperature.