The hydrostatic pressure-induced transition phase of ScSb from the sixfold-coordinated NaCl-type (B1) to the eightfold-coordinated CsCl-type (B2) is investigated within the Perdew-Burke-Ernzerhof (PBE) form of generalized gradient approximation. It is found that the transition pressure from the B1 to B2 phase is at 42.8 GPa which agrees with experiment. Through the quasi-harmonic Debye model, the dependences of the relative volume V on the pressure P, the thermal expansion, the Gruneisen parameter ratio, (gamma - gamma (0))/gamma (0), the Debye temperature I similar to, and heat capacity C (V) on the pressure P and temperature T are estimated. The quasi-harmonic Debye model for the first time is used to predict phase diagram of B1 -> B2.