This work is performed to prepare new sponge nanocomposites for improving energy storage performance to satisfy cheap cost and high power. Natural rubber/ethylene propylene diene rubber (NR/EPDM) and an adhesion/lamination on cotton with different nanofillers, hexagonal boron nitride (h‐BN), graphene oxide (GO), and vanadium oxide (V2O5) and subsequent are prepared and irradiation under electron beam radiation to fulfill supercapacitor criteria. The electrochemical performance is measured by three methods, cyclic voltammetry, galvanostatic charge/discharge, and electrochemical impedance spectroscopy. The results show that the sponge nanocomposite of NR/EPDM/h‐BN has the highest tensile strength compared to the other sponge nanocomposites. The sponge nanocomposite of NR/EPDM/h‐BN/GO has the advantages of foam‐like porosity, high foaming degree, good flexibility, and enhanced durability, which cooperatively results in excellent electrochemical behaviors, as a result of improved charge‐transfer, to satisfy the supercapacitor criteria. The cotton adhesion compatibility is affirmed through both Fourier transform infrared, X‐ray diffraction and scanning electron microscopy. The mechanical properties, electrochemical performance, and thermal resistance of the sponge NR/EPDM nanocomposites laminated to cotton are remarkably improved at 150 kGy, over the unirradiated sponge nanocomposites. The sponge NR/EPDM/h‐BN/GO nanocomposite‐based supercapacitor demonstrates a high specific capacitance of 55 F g−1 at a high current density of 1 A g−1, also displays excellent cycling stability, retention of ≈97% of its starting capacitance charge–discharge cycles after 1000 at 150 kGy.