Diagram of the phase transformation behavior of GeS2-Ga2S3-CsI glasses is realized in this article and the structure-property dependence of the chalcogenide glasses is elucidated using differential scanning calorimetry and Raman spectroscopy. We observe the compositional threshold of crystallization behavior locates at x=6-7mol% in (100-x)(0.8GeS2-0.2Ga2S3)-xCsI glasses, which is confirmed by the thermodynamic studies. Structural motifs are derived from the Raman result that [Ge(Ga)S4], [S2GeI2], [S3GaI], and [S3Ga-GaS3] were identified to exist in this glass network. Combined with the information of structural threshold, local arrangement of these structural motifs is proposed to explain all the experimental observations, which provides a new way to understand the correlation between crystallization behavior and network structure in chalcogenide glasses.