We perform systematic first-principles calculations to investigate the spin-phonon coupling (SPC) of Cr2Ge2Te6 (CGT) monolayer (ML). It is found that the Eg phonon mode at 211.8 cm^{-1} may have a SPC as large as 3.19 cm^{-1}, as it directly alters the superexchange interaction along the Cr-Te-Cr pathway. Furthermore, the strength of SPC of the CGT ML can be further enhanced by an in-plane compressive strain. These results provide useful insights for the understanding of SPC in novel two-dimensional magnetic semiconductors and may guide the design of spintronic and spin Seebeck materials and devices.
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