To find new chalcogenide glass possessing larger second-order non-linearity,glasses with compositions Ge-Ga-X-S (X=P,As,Sb) were prepared via melt quenching technique. The amorphous nature of all the compositions of the as-quenched glasses was confirmed by X-ray diffraction(XRD). The glassy thermal properties of the as-quenched glasses were established by differential thermal analyses(DTA). The glass structure was studied by RAMAN spectra and the second order nonlinearity was studied by the Maker Fringe method after the electron beam poling(EBP) and electric/temperature field poling(ETFP) respectively. Additions of various pnicogen atoms into the Ge-Ga-S glasses lead to the difference in the second order nonlinearity of the glass. Its found that glasses with different structures result in different SHG intensities,and even more,a large second order nonlinear susceptibility c(2) of about 9 pm/V was obtained for all the glasses and the reasons for such a large susceptibility were analyzed.