The performance of graphene can be influenced by its surface mophology, while the surface morphology of graphene is closely related to the substrate. The adsorption and peeling process of graphene on a corrugated surface can provide a theoretical basis for the functional preparation and transfer of graphene. In this work, the adhesion properties and peeling process of graphene on nanostructured substrate are investigated by using molecular dynamics (MD) simulation. As an effective tool of atomic collision theory, MD simulation can provide detailed information about the adsorption configuration and peeling properties of graphene on the nanostructure surface, making up for the deficiency of experiment. The results indicate that graphene can conformably coat on the surface, partially adhere to or remain flat on the top of the stepped substrate. We find that the continuous transition occurs in the adsorption configuration of graphene on the stepped substrate, but the repeated process appears in the transition from partial adherence to conformable coating. When graphene coats on the nanostructured substrate conformably, the adsorption energy can reach its peak value. The adsorption configuration of graphene can change from suspension to partial adhesion after the adsorption energy has exceeded 360 eV -2. It is also shown that the average peeling force fluctuates periodically when the absorption configuration of graphene is conformably coated or suspended on the stepped substrate. Two kinds of behaviors can be noticed in the peeling process. The graphene can directly slide over the bottom while it is fully coated on the surface. The graphene is separated directly from the corrugated surface while it suspends or partially adheres to the surface. If the absorption configuration of graphene is in the suspension state, the average peeling force appears to change drastically within a section of peeling distance and then decreases immediately below zero. Although the flexural stiffness of graphene can be overcome, the interfacial friction between graphene and the substrate is also an essential factor affecting the final adsorption configuration. In this paper, we propose a theoretical formula for the average peeling force according to the changes of size parameters on the nanostructured substrate. The theoretical formula is validated by the simulation results. In addition, with the increase of peeling angle, the average peeling force first increases and then becomes smaller. As a result, a larger average peeling force can be found when the graphene with Stone-Wales defect structure is peeled from the flat substrate. With the increase of double vacancy defect, the maximum peeling force decreases in a certain range, whereas it increases beyond this range. This work can provide a theoretical reference for exploring the peeling property and the adhesion mechanism of graphene on nanostructure surface.