We　investigate　a　giant　magnetoresistance　(MR)　effect　in　periodic,　asymmetric　magnetic　superlattices　(MSLs)　on　graphene.　The　MR　ratio　shows　a　strong　dependence　on　both　the　interval　of　magnetic　barriers　and　the　asymmetry　degree　of　the　structures.　With　the　increase　of　the　number　of　periods,　there　is　only　one　MR　peak　and　the　drift　of　the　position　of　the　peak　appears　around　a　specific　Fermi　energy.　The　highest　value　of　the　maximal　MR　ratio　can　be　up　to　10(17)%.　Our　studies　indicate　that　the　graphene-based　asymmetric　MSLs　structure　is　an　ideal　candidate　of　a　giant　MR　device,　e.　g.,　the　magnetic　reading　device.　(C)　2012　American　Institute　of　Physics.　[http://dx.doi.org/10.1063/1.4757881]