Graphene　quantum　dots　(GQDs),　as　a　new　kind　of　carbon　nanomaterial,　have　been　widely　prepared　with　graphene　oxide　(GO)　as　precursor　via　various　methods.　However,　little　work　has　been　done　to　detail　the　structural　relationship　between　GQDs　and　pristine　GO.　Herein,　we　synthesized　GQDs　through　acidic　oxidation　of　GO　and　separated　blue-photoluminescent　GQDs　(b-GQDs)　and　green-photoluminescent　GQDs　(g-GQDs)　by　a　simple　dialysis　technique.　Although　the　transmission　electron　microscopy　(TEM)　and　atomic　force　microscopy　(AFM)　images　reveal　their　similar　morphology,　the　results　of　X-ray　photoelectron　spectroscopy　(XPS),　Fourier-transform　infrared　(FTIR)　spectroscopy,　Raman　spectroscopy　and　zeta　potential　measurements　reveal　their　distinct　structures　with　different　origins　from　the　GO.　The　b-GQDs　may　originate　from　the　intact　sp(2)　cluster　of　GO,　while　the　g-GQDs　are　derived　from　the　relaxed　carbon　backbone　with　numerous　oxygen-containing　functional　groups.　Besides　photoluminescence　(PL)　properties,　the　peroxidase-like　catalytic　activity　of　the　two　GQDs　was　also　compared.　Interestingly,　the　g-GQDs　exhibit　higher　peroxidase-like　catalytic　activity　and　can　be　used　to　detect　H2O2　with　a　detection　limit　of　87　nM,　which　is　lower　than　most　other　reported　methods.　We　believe　this　work　provides　important　insights　into　the　structure,　PL　properties　and　potential　applications　of　GO-derived　GQDs.