Chalcogenide glasses in the Na2S-GeS2-Ga2S3 pseudoternary system were synthesized using a combination route of melt-quenching and mechanical-milling methods. First, a glass rich in germanium (90GeS2-10Ga2S3) is synthesized by melt-quenching synthesis in a silica tube sealed under vacuum. This glass is used as a precursor for the second step of mechanochemistry to explore the Na2S-GeS2-Ga2S3 pseudoternary system. By using this synthesis route, the glass-forming ability is improved as the vitreous domain is enlarged, especially for Na- and Ga-rich compositions. The as-obtained amorphous powders are characterized by Raman spectroscopy, differential scanning calorimetry, X-ray total scattering, and pair distribution function (PDF) analysis. The evolution of the Raman features observed is reproduced using density functional theory calculations. Impedance spectroscopy was performed to determine the conductivity of the new glasses. The addition of germanium sulfide to the Na2S-Ga2S3 pseudobinary system enables one to increase the conductivity by 1 order of magnitude. The highest room-temperature ionic conductivity, as measured by impedance spectroscopy, is 1.8 × 10-5 S·cm-1.