The interfacial resistance and capacitance in pellets made from GeS2-Ga2S3-Li2S-LiI glass powder are studied under uniaxial compression. By varying the pressure, remarkable change in the geometric dimension of the interfacial resistance and capacitance is observed. Assuming that the interfacial resistance and capacitance arise from the contact region between the powder particles, a quantitative model is established that well describes the geometric dimension change in the interfacial resistance and capacitance. This work emphasizes that ameliorating the contact between the particles is one of the most important methods to reduce the interfacial resistance in the powder-type ionic-conduction devices made from highly-conductive sulfide solid electrolyte powders.