The electronic structure of strontium aluminate, SrAl2O4, is calculated by using the scalar-relativistic full potential linearized augmented plane wave (FLAPW) method. SrAI(2)O(4) is predicted to be an indirect-gap material, since the valence band maximum locates near Z point and the conduction band minimum at F point. The valence band with the width ca. 5.3 eV is mainly constructed from 0 2p orbitals, where AI 3s3p and Sr 5s5p slightly hybridize with 0 2p, and the lower conduction band from Sr 5s orbitals.