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Ge-Ga-Ag-S chalcogenide glasses with the composition Ge30Ga3Ag4S63 were obtained by the conventional melt-quenching method. According to the visible-infrared and infrared spectra,Ge30Ga3Ag4S63 chalcogenide glass possesses wide transmittance window from 510 nm in the visible region up to 11.5 ìm in the infrared region. And the present glass has better glass-forming ability (the difference between glass transition temperature and the peak temperature of crystallization is larger than 100 ℃). Utilizing maker-fringe technique,a prominent second-harmonic generation was observed in Ge30Ga3Ag4S63 chalcogenide glass after irradiated by an electron beam (Accelerating voltage: 25 kV:Irradiating current: 15 nA:Irradiating time: 10 min). And the mechanism of second-harmonic generation in the Ge-Ga-Ag-S system glasses was discussed.