As a new category of quasi-one-dimensional materials, graphene nanoscroll (GNS) has captivated the researchers recently because of its exceptional electronic properties like having large carrier mobility. In addition, it is admitted that the scrolled configurations for graphene indicate larger stability concerning the energy, as opposed to their counterpart planar configurations like nanoribbon, nanotube, and bilayer graphene. By utilizing a novel analytical approach, the current paper introduces modeling of the density of state (DOS), carrier concentration, and quantum capacitance for graphene nanoscroll (suggested schematic perfect scroll-like Archimedes spiral). The DOS model was derived at first, while it was later applied to compute the carrier concentration and quantum capacitance model. Furthermore, the carrier concentration and quantum capacitance were modeled for both degenerate and nondegenerate regimes, along with examining the effect of structural parameters and chirality number on the density of state and carrier concentration. Latterly, the temperature effect on the quantum capacitance was studied too.