We fabricated positively charged functional polyacrylamide hydrogel by copolymerization of acrylamide-containing amines and sole acrylamides. Such hydrogel can have high affinity with negatively charged DNA and later we combine this chemistry with a graphene nano platform. That is, we successfully fabricated a graphene nanopore supported on a glass micropore inside hydrogel using pulsed voltage fabrication method, which suggests a new avenue for realizing cost-efficient, high-performance graphene nanodevices. With such a glass micropore supported graphene-hydrogel system, we found that the low frequency noise of the graphene nanopore inside hydrogel is much lower than the one that without hydrogel. DNA translocation experiments performed on this electrical pulse fabricated graphene-on-glass (GOG) nanopore, demonstrated the suitability of the GOG nanopore for single molecule measurements. Strikingly, compared to previously reported translocation time on ssDNA in solid state nanopores, the results on hydrogel functionalized GOG nanopores indicate deceleration of DNA translocation as much as one order of magnitude.