This　paper　addresses　multi-window　Gabor　frames　with　rational　time-frequency　product.　Such　issue　was　considered　by　Zibulski　and　Zeevi　(Appl.　Comput.　Harmonic　Anal.　4　(1997),　188-221)　in　terms　of　Zak　transform　matrix　(so-called　Zibuski-Zeevi　matrix),　and　by　many　others.　In　this　paper,　we　introduce　of　a　new　Zak　transform　matrix.　It　is　different　from　Zibulski-Zeevi　matrix,　but　more　direct　and　convenient　for　our　purpose.　Using　such　Zak　transform　matrix　we　characterize　rational　time-frequency　multi-window　Gabor　frames　(Riesz　bases　and　orthonormal　bases),　and　Gabor　duals　for　a　Gabor　frame.　Some　examples　are　also　provided,　which　show　that　our　Zak　transform　matrix　method　is　efficient.