Abstract We have investigated the electronic structures of the LiYF 4 containing interstitial fluorine atoms and F center (a fluorine ion vacancy trapping an electron) using first-principles density functional theory. It is found that the interstitial fluorine atoms in two different interstitial positions would combine with its nearest neighbor two or three formal lattice fluorine ions forming fluorine molecular ions F 3 2 − or F 4 3 − by different ways, which would cause the 260 nm absorption band. Simultaneously, our study indicates that one electronic state appears in the forbidden band of the perfect LiYF 4 crystal resulting from the F center in the LiYF 4 crystal. And the energy difference of this electronic state and the bottom of the conduction band is 3.74 eV, corresponding to the 331 nm absorption band. It is predicted that the 330 nm absorption band could arise from the F center in LiYF 4 crystals.