Due　to　their　potential　applications　in　multiplexing　techniques,　superframes　(also　called　vector-valued　frames)　and　subspace　frames　have　interested　many　mathematicians　and　engineering　specialists.　A　weak　bi-frame　is　a　generalization　of　a　bi-frame　in　a　Hilbert　space.　This　paper　addresses　vector-valued　subspace　weak　Gabor　bi-frames　(WGBFs)　on　periodic　subsets　of　the　real　line,　that　is,　WGBFs　for　L2(S,　CL)　with　S　being　periodic　subsets　of　R.　Using　Zak　transform　matrix　method,　we　obtain　a　characterization　of　WGBFs,　which　reduces　constructing　WGBFs　to　designing　Zak　transform　matrices　of　finite　order;　present　an　example　theorem　of　WGBFs;　and　derive　a　density　theorem　for　WGBFs.　©　2018,　Chinese　Academy　of　Sciences.　All　right　reserved.