Detailed density functional theory(DFT)calculations of the structural,mechanical,thermodynamic,and electronic properties of crystalline CaF2 with five different structures in the pressure range of 0 GPa-150 GPa are performed by both GGA(generalized gradient approximation)-PBE(Perdew-Burke-Ernzerhof)and LDA(local density approximation)-CAPZ(Cambridge Serial Total Energy Package).It is found that the enthalpy differences imply that the fluorite phase→ PbCl2-type phase → Ni2In-type phase transition in CaF2 occurs at PGGA1 = 8.0 GPa,PGGA2 = 111.4 GPa by using the XC of GGA,and PLDA1 = 4.5 GPa,PLDA2 = 101.7 GPa by LDA,respectively,which is consistent with previous experiments and theoretical conclusions.Moreover,the enthalpy differences between PbCl2-type and Ni2In-type phases in one molecular formula become very small at the pressure of about 100 GPa,indicating the possibility of coexistence of two-phase at high pressures.This may be the reason why the transition pressure of the second phase transition in other reports is so huge(68 GPa-278 GPa).The volume changed in the second phase transition are also consistent with the enthalpy difference result.Besides,the pressure dependence of mechanical and thermodynamic properties of CaF2 is studied.It is found that the high-pressure phase of Ni2In-type structure has better stiffness in CaF2 crystal,and the hardness of the material has hardly changed in the second phase transition.Finally,the electronic structure of CaF2 is also analyzed with the change of pressure.By analyzing the band gap and density of states,the large band gap indicates the CaF2 crystal is always an insulator at 0 GPa-150 GPa.