Based on numerical simulations and experimental studies, we show that a composite material which consists of a sheet of graphene on a Au(111) surface exhibits both an excellent conductivity and the ability to stably adsorb biomolecules. If we use this material as a substrate, the signal-to-noise ratios can be greatly enhanced. The key to this unique property is that graphene can stably adsorb carbon-based rings, which are widely present in biomolecules, due to π-stacking interactions while the substrate retains the excellent conductivity of gold. Remarkably, the signal-to-noise ratio is found to be so high that the signal is clearly distinguishable for different nucleobases when an ssDNA is placed on this graphene-on-Au(111) material. Our finding opens opportunities for a range of bio/nano-applications including single-DNA-molecule-based biodevices and biosensors, particularly, high-accuracy sequencing of DNA strands with repeating segments.