The　notion　of　weak　dual　frames　is　a　generalization　of　that　of　dual　frames.　Gabor　analysis　on　discrete　periodic　sets　has　potential　applications　in　signal　processing.　This　paper　addresses　vector-valued　weak　Gabor　dual　frames　on　discrete　periodic　sets.　We　introduce　the　notions　of　its　weak　oblique　Gabor　dual,　weak　Gabor　duals　of　types　I　and　II　for　a　Gabor　system　on　a　discrete　periodic　set.　Using　the　Zak-transform　matrix　method,　we　characterize　these　three　kinds　of　weak　duals　and　their　uniqueness.　Finally,　we　give　an　explicit　expression　of　a　class　of　weak　Gabor　duals　and　provide　some　examples.　Published　under　license　by　AIP　Publishing.