In the current study, the effects of different graphene (Gr) parameters on the interfacial properties of graphene reinforced thermoplastic polyurethane (Gr/TPU) nanocomposites have been assessed by the atomistic simulation, in particular, molecular dynamics (MD) simulations. To explore the enhancement mechanisms of interfacial mechanical strength of the Gr/TPU nanocomposite, constant strain method is used and the pull-out simulation process (both normal and transverse direction) between TPU and Gr is carried out, examined and interpreted. The results show that the transverse failure may be much easily compared to the normal failure in case of a flat Gr-based nanocomposite. For a flat single-layer Gr of size (1.5 nm x 1.7 nm), the shear pull-out force is found to be nearly 100 kcal/mol/nm while that for the normal pull-out case is nearly 600 kcal/mol/nm. Stronger molecular bindings happen between the wrinkled Gr and the polymer matrix to result in a higher shear pull-out force (nearly 700 kcal/mol/nm). Moreover, it is observed that pull-out of a single Gr layer from the polymer nanocomposite is found to be much easier than in case of multilayer Gr. The Gr sheet having Stone-Wales (SW) type defect is found to play a better role in enhancing the interfacial properties in nanocomposites than single-vacancy (SV) or double-vacancy (DV) type defective Gr sheets, as discussed later. Pristine Gr structures exhibit lesser tendency to increase interfacial shear strength than surface functionalized Gr structures.