The composite hydrogel electrolytes developed from conducting polymers own superb/excellent conductive, self-healing, and mechanical properties. However, it is still challenging to exploit them in energy storage devices. To address this issue, novel poly(acrylamide)/poly(3,4-ethylenedioxythiophene): poly(styrene sulfonate) (PEDOT:PSS) composite hydrogel electrolytes were developed through free radical polymerization in which sodium montmorillonite clay was added as a physical crosslinker. The different amounts of PEDOT:PSS were added to the composite hydrogel electrolytes. The structure of the synthesized composite hydrogel electrolytes was investigated by X-ray diffraction (XRD) analysis. The surface morphology of the composite hydrogel electrolyte was examined with the field emission scanning electron microscopy (FESEM) and elemental composition was determined using energy-dispersive X-ray spectroscopy (EDX). The ionic conductivity was measured at ambient temperature. Among the synthesized electrolytes, PEDOTAAM34 achieved the highest ionic conductivity of 13.7 × 10−3 S/cm at room temperature. Furthermore, electrochemical studies were performed by sandwiching the composite hydrogel electrolytes between symmetric carbon-coated graphite electrodes. The fabricated AC/PEDOTAAM34/AC based symmetric supercapacitor attained the highest specific capacitance of 327 F/g at 3 mV/s and 385.4 F/g (energy density of 53.57 Wh/kg at a power density of 100.08 W/kg) at 100 mA/g current density. The self-healable characteristics of symmetric supercapacitors were confirmed by powering up a light-emitting diode (LED).