Graphene[1], widely known as single layered graphite, has generated lot of interests as generation next electronic material since its practical existence as free standing film. Its structural flexibility provides an opportunity to tune its electronic properties from being semimetal to semiconductor [2,3] for the fabrication of nanoscale devices[4]. Graphene nanoribbons (GNR) are defined as stretched graphene with straight edges and they transform from semiconductor to semimetal as the width of the ribbon changes and hence offer a variety of graphene. While there have been increasing interest in elucidating graphene nano-scale structures the development of a reproducible nanostructured assembly of graphene (nanoribbon) and DNA that could potentially lead to controllable and manipulative nano-scale mechanical devices have been very less explored. Recently Razdan, Patra and co-workers[5] have developed self assembled carbon nanotube-conducting polymer fibers. Also Sinha and members of his research group have a provisional patent and a pending patent application on a biosensor whose principle is based on the Carbon Nanotube (CNT)/DNA interaction. We will build on from the understanding on the previous work to establish a reproducible graphene- DNA nanostructured assembly that may consequently help develop graphene-DNA based biodevices. We plan to understand the attachment of graphene with single-stranded DNA by a self-assembly process under strong ultrasonication and in the resulting water-dispersible graphene-DNA hybrids. We intend to achieve monolayers of ss-DNA molecules adsorbed on both sides of the graphene sheets by a non-covalent stacking and other secondary forces that will eventually lead to development of graphene-DNA based devices in the long run.