A basic nature of cubic Ag4Hf3S8 for electrochemical Li insertion was examined with relation to cell properties and Rietveld analyses for es-situ X-ray powder diffraction patterns observed at several discharge steps. The composition dependence of cell voltage curves observed in the closed type Li/1M-LiPF6 in PC/Ag4Hf3S8 cell showed a long plateau at around 2.2-2.0 V up to LixAg4Hf3S8 (x less than or equal to 3). The cell voltage decreased with an increase of Li intercalation and final lithiated phase was assigned to cubic LixAgyHf3S8 (x > 3, x + y = 7). The electrochemical lithiation of Ag4Hf3S8 at low constant current densities proceeded topochemically. The structures of lithiated phases were solved without changing the space group P4(3)32 (No. 212) for Ag4Hf3S8 host, indicating that Hf3S8 framework structure was kept through the Lithiation.