The electronic structures of alkaline-earth fluoro-halides - SrFBr, SrFI, and CaFBr, which crystallize in the PbFCl-type structure - have been studied using the tight-binding linear muffin-tin orbital method within the local density approximation. The total energies were calculated using the atomic sphere approximation and were used to determine the ground state properties of these systems. The calculated ground state properties agree fairly well with the experimental results. These systems were found to be direct band gap insulators. The pressure dependence of the band gap was also studied. The band gap closes at high pressures leading to band overlap. A possible reason for the metallization in these compounds is discussed.