The hydrostatic-pressure-induced transition phase of BaS from the NaCl-type structure (B1) to the CsCl-type structure (B2) is investigated by ab initio plane-wave pseudopotential den-sity functional theory method. It is found that the transition pres-sure from B1 to B2 phases is 8.2 GPa according to the usual con-dition of equal enthalpy. Through the quasi-harmonic Debye model,the dependences of the relative volume V/V0 on the pres-sure P,the thermal expansion parameter ratio on pressure P,and the Debye temperature Θ and heat capacity CV on pressure P and temperature T are estimated.