First principles calculation of LiF and NaF (NaCl phase and CsCl phase) underhigh pressure was carried out with the full potential linearized augmented plane wave plus local orbital method. It was shown that NaCl-type LiF transforms to a CsCl-type phase at about 450 GPa. Calculations of the electronic properties of LiF at high pressure compared with the energy band structural information indicate that a non-structureal transition occurs at about 53GPa, in which the direct band structure transforms to an in-direct band structure. We also calculated the complex electronic dielectric function and the static dielectric constants of LiF as functions of pressure. The results obtained for LiF are also compared with siilar data of NaF system.