Due　to　its　potential　applications　in　multiplexing　techniques　such　as　time　division　multiple　access　and　frequency　division　multiple　access,　superframe　has　interested　some　mathematicians　and　engineering　specialists.　In　this　paper,　we　investigate　super　Gabor　systems　on　discrete　periodic　sets　in　terms　of　a　suitable　Zak　transform　matrix,　which　can　model　signals　to　appear　periodically　but　intermittently.　Complete　super　Gabor　systems,　super　Gabor　frames　and　Gabor　duals　for　super　Gabor　frames　on　discrete　periodic　sets　are　characterized;　An　explicit　expression　of　Gabor　duals　is　established,　and　the　uniqueness　of　Gabor　duals　is　characterized.　On　the　other　hand,　discrete　periodic　sets　admitting　complete　super　Gabor　systems,　super　Gabor　frames,　super　Gabor　Riesz　bases　are　also　characterized.　Some　examples　are　also　provided　to　illustrate　the　general　theory.