Chalcohalide glasses with compositions of (100-2x) GeS2-xGa2S3-xCsCl (x= 15, 20, 25) are synthesized by the conventional melt-quenching method. Third-order optical nonlinearities of these glasses are studied using the Z-scan technique. The relationship between photon energy and optical nonlinearity is analyzed. Moreover, the effect of glass composition on the third-order nonlinearity is investigated. The results show that just a small variation of the excitation photon energy causes the value of samples to change in a large range. The value increases with the enhancement of excitation photon energy. When the photon energy is close to 0.5 Eg, the value is close to 0 and the factor of quality of the glass reaches an optimal value. The increase of CsCl content enlarges the optical band gap Eg, which leads to the blue-shift toward the short edged wavelength, and lowers the value. However, the value varies little because of the opposite effect on the optical nonlinearity between the structure and the band gap Eg. In this work, the optical nonlinearity is shown to be dependent on band gap and structure, and the results have a certain directive significance and reference value for future research.