A nanophase soild CaF2 which has clean interface and average graininess 16 nm was prepared with the method of evaporation in inert gas and being pressed in high vacuum, complex impedance spectra of nanophase CaF2 were measured precisely using 70 frequencies from 100 kHz to 100 Hz under the different hydrostatic pressure from 0.1～2 400 MPa. Variations of both ionic conductivity and dielectric constant in nanophasc CaF2 with pressure were given. It is indicated in final discussion that passage for migration of fluorine ions being compressed is the main factor of changing pressure-effect on ionic conductivity. Under low pressure the passage sizes much larger than optimum, so movement of F- is not the fastest. Under 1 263 MPa pressure, the passage size reaches its optimum, migration of F- is the easiest, hence reaches maximum. When pressure is over 1 263 MPa, the passage size becomes smaller and smaller than optimum, migration of F- gets more and more difficult, so that diminishes rapidly. Besides, polarization of space charge on interface layer is the cause which makes relative dielectric constant of nanophase CaF2 larger. From the role of interface we can understand the pressure effect of the dielectric constant.