We investigate the phase transition pressure, elastic and thermodynamic properties of CaPo by the first-principles plane wave pseudo-potential method in the framework of density functional theory. By the isoenthalpy principle, the phase transition pressure from B1 structure to B2 structure is found to be about 22.8GPa. From the high pressure elastic constants obtained, we find that the B1 structure CaPo is unstable when the applied pressure is larger than 20 GPa, which is in good agreement with the results from the isoenthalpy principle. Moreover, the thermodynamic properties of pressure and temperature of B1 structure CaPo(including specific heat capacity, the Debye temperature, thermal expansion and Grüneisen parameter) are also successfully obtained.