Understanding of how to integrate DNA molecules with graphene materials is important for the development of biosensors and biomolecular logic circuits. For some of these applications, controlling DNA structural conformation on the graphene substrate is critically important and can be achieved through the use of self-assembled monolayers. Here, we performed all-atom molecular dynamics simulations to understand how various 1-octadecylamine (ODA) coatings of the graphene surface affect the conformation of double-stranded DNA (dsDNA) on the surface. The simulation results demonstrated that dsDNA structures become more stable as ODA concentration increases due to the formation of DNA-ODA hydrogen bonds and reduction of DNA-surface interactions, which aid in retaining internal DNA interactions. Specifically, the interaction of ODA molecules with DNA prevents nucleobases from forming pi-pi stacking interactions with the surface. Some dsDNA conformations, such as sharp kinks or unwinding, can occur more frequently in DNA with A-T sequences due to weaker pairing interactions than with G-C sequences. Furthermore, our results conclude that both DNA sequence and ODA concentration play an essential role in experimentally observed conformational changes of DNA on the graphene surface.