The present work summarizes the fabrication of an amine-functionalized cadmium-based metal-organic framework (MOF), {[Cd(AT)(BP)]·4DMF}n or Cd_AT-BP, by adopting a simple solvothermal approach using 2-aminoterephthalic acid (AT) as the main linker, while 4,4'-bipyridyl (BP) as an auxiliary linker. The structure of Cd_AT-BP was validated by the single-crystal X-ray diffraction technique that revealed the formation of an overall three-dimensional network with BP acting as a bridge between the 2D sheets of the MOF. The robust framework of Cd_AT-BP decorated with a free amine functional group was utilized for energy storage application. The electrochemical measurements of Cd_AT-BP revealed a maximum areal capacitance of 9.8 mF/cm2 at a scan rate of 5 mV/s. Further, to enhance the practical utility of Cd_AT-BP in energy storage devices, two composites of Cd_AT-BP with reduced graphene oxide (rGO) and multiwalled carbon nanotubes (CNTs), viz., Cd_AT-BP/rGO and Cd_AT-BP/CNT, were prepared by adopting a facile ultrasonication approach. The synthesized Cd_AT-BP/rGO and Cd_AT-BP/CNT composites displayed an impressive areal capacitance of 117 and 37 mF/cm2 (58.5 and 17.5 F/g) at a scan rate of 5 mV/s, respectively, and a capacitance retention of up to 118 and 100% after 5000 cycles at a constant current density of 5 mA/cm2. The highest energy density of about 4.23 mW h/cm2 (2.12 W h/kg) at a current density of 1 mA/cm2 was shown by Cd_AT-BP/rGO among all the three materials attributable to the layered structure of rGO, providing a larger surface area accessible for ion adsorption. Enticed by the remarkable outcomes exhibited by Cd_AT-BP/rGO, we fabricated a two-electrode asymmetric supercapacitor (ASC) device. The developed ASC device revealed energy and power densities of 26.7 mW h/cm2 (13.4 W h/kg) and 3760 mW/cm2 (1880 W/kg), respectively, with a galvanostatic charge-discharge stability of up to 10,000 cycles. The findings identify Cd_AT-BP/rGO as a potential contender for future-generation supercapacitors.