The　high-pressure　behaviors　of　crystalline　(Ba0.5Sr0.5)　TiO3　(BST)　are　investigated,　using　the　first-principles　calculations　based　on　the　density　functional　theory.　The　results　show　that　as　pressure　increases,　the　band　gap　of　BST　first　increases　and　peaks　at　around　55　GPa,　and　then　gradually　decreases.　The　analysis　of　density　of　states　shows　that　in　the　low-pressure　region　(0　＜　P　＜　55　GPa);　the　increase　in　band　gap　is　due　to　the　formation　of　anti-bonding　states　and　bonding　states　in　the　conduction　band　and　valence　band,　respectively.　In　the　high-pressure　region　(P　＞　55　GPa),　the　delocalization　phenomenon　in　dominant　due　to　the　fact　that　the　delocaligation　action　exceeds　the　force　of　bonding　state　and　anti-bonding　state,　which　results　in　the　decrease　of　the　band　gap.