We report a study on the relationship between the structure and electron transport properties of nanoscale graphene/pentacene interfaces. We fabricated graphene/pentacene interfaces from 10 to 30 nm thick needle-like pentacene nanostructures down to two-three layer (2L-3L) dendritic pentacene islands, and we measured their electron transport properties by conductive atomic force microscopy (C-AFM). The energy barrier at the interfaces, i.e., the energy position of the pentacene highest occupied molecular orbital (HOMO) with respect to the Fermi energy of graphene and the C-AFM metal tip was determined and discussed with an appropriate electron transport model (a double Schottky diode model and a Landauer-Buttiker model, respectively) taking into account the voltage-dependent charge doping of graphene. In both types of samples, the energy barrier at the graphene/pentacene interface is slightly larger than that at the pentacene/metal tip interface, resulting in 0.47-0.55 eV and 0.21-0.34 eV, respectively, for the 10-30 nm thick needle-like pentacene islands, and 0.92-1.44 eV and 0.67-1.05 eV, respectively, for the 2L-3L thick dendritic pentacene nanostructures. We attribute this difference to the molecular organization details of the pentacene/graphene heterostructures, with pentacene molecules lying flat on graphene in the needle-like pentacene nanostructures, while standing upright in the 2L-3L dendritic islands, as observed from Raman spectroscopy.