Previously reported chalcogenide glass Raman fiber lasers are made of glass compositions such as As2S3 or As2Se3. However, due to the high toxicity of the element arsenic, there is a potential risk in the glass preparation, fiber drawing, and testing processes. Therefore, we need to explore new environmentally friendly chalcogenide glasses that do not contain As for Raman fiber lasers. Studies have shown that the chalcogenide glasses of Ge-Sb-Se system have excellent infrared transmissions and good environmental friendliness, and thus they are excellent candidates for chalcogenide glass Raman fiber lasers. However, their Raman gains have not been reported. Then Raman gain coefficients can be obtained by experimental measurements and theoretical analyses. The experimental method requires expensive laboratory equipments, a complex optical path, and precision adjustments. Therefore, the design and preparation of new chalcogenide glass fiber with high Raman gain require the theoretical analysis of the Raman gain characteristics in a particular glass component glass. In this work, four chalcogenide glasses, respectively, with compositions of As2S3, As2Se3, Ge20Sb15Se65 and Ge28Sb12Se60 (mol%) are prepared. Refractive indices, infrared transmission and Raman spectra of these glass samples are measured. By using spontaneous Raman scattering theory combined with the measured Raman spectral data, the values of Raman gain coefficient gR of the chalcogenide glasses are calculated and calibrated by a quartz glass sample. Results show that the gR of As2S3 glass is 6010-13 m/W at 230 cm-1 Raman shift and the gR of As2Se3 glass is 22310-13 m/W at 340 cm-1 Raman shift, which are consistent with the experimental results reported in the literature. Compared with the traditional method, the present method used for calculating the fiber Raman gain coefficient provides great convenience for exploring new chalcogenide glasses with high Raman gain. By using this method, we obtain the gR values of Ge20Sb15Se65 and Ge28Sb12Se60glasses at 200 cm-1 Raman shift, which are 21510-13 m/W and 11110-13 m/W respectively. Meanwhile, we analyze the effects of composition and network structure of chalcogenide glass samples on the Raman gain coefficient and gain spectrum. There are two Raman peaks at 165 cm-1 and 200 cm-1 Raman shift, which are attributed to Ge-Ge bond vibration and Ge-Se bond vibration of common apex GeSe4/2 tetrahedral structure respectively. It could be found that the Raman gain coefficient of Ge20Sb15Se65 glass is bigger than that of Ge28Sb12Se60glass at 200 cm-1 Raman shift because of more Ge-Se bonds. By further optimizing the ratio of components of Ge-Sb-Se chalcogenide glass, we could obtain higher Raman gain coefficient at a particular frequency shift. These results show that the Raman gain coefficient of Ge-Sb-Se chalcogenide glass without poisonous element is up to over 200 times that of the ordinary quartz glass, which provides a new possibility for environment-friendly Raman fiber laser material.