Ultracapacitors are promising candidates for alternative energy storage applications since they can store and deliver energy at relatively high rates. Here, we present hybrid nanocarbon ultracapacitor electrodes with a low equivalent series resistance (ESR) of 7 ohms. 1-pyrenebutyric acid treated large-area single layer graphene (SLG) sheets covered with shortened multi-walled carbon nanotubes (MWNTs) have been utilized as highly conductive and percolated networks of hybrid carbon nanomaterial composites or thin films as ultracapacitor electrodes. Uniform centimeter scale single layer graphene sheets were produced via low pressure chemical vapor deposition using copper foil substrates and then subsequently modified by 1-pyrenebutyric acid functionalization. Chemically shortened MWNTs ranging in length of 200-500 nm, were deposited by drop casting on 1-pyrenebutyric acid functionalized SLG films. SLG/MWNT nancomposite hybrid films of different thicknesses were obtained by controlling the density of MWNT suspension. Surface morphology and nanostructure of the hybrid nanocomposites indicated relatively dense and homogeneous web-like networks. Specific capacitance values of the hybrid electrodes were substantially increased by 200% compared to those ultracapacitors fabricated using buckypaper electrodes. Average values of specific capacitance and energy density obtained were 140.64 F/g and 21.54 Wh/kg respectively. SLG/MWNT nanocomposite electrodes are very promising for future ultracapacitor devices with their low ESR value that is 95% lower than that of buckypaper based ultracapacitors.