The phase transition of SrS from NaG1 structure (B1) to CsCl structure (B2) is investigated by means of ab initio plane-wave pseudopotential density functional theory, and the thermodynamic properties of the B1 and the B2 structures are obtained through the quasi-harmonic Debye model. It is found that the transition phase from the B1 to the B2 structures occurs at 17.9 GPa, which is in good agreement with experimental data and other calculated results.Moreover, the thermodynamic properties (including specific heat capacity, the Debye temperature, thermal expansion and Grüneisen parameter) have also been obtained successfully.