The present article focuses on the development of a highly ion-conductive, solvent-free, solid-state polymer electrolyte membrane (PEM) via photopolymerization of polyethylene glycol diacrylate (PEGDA) network from its homogeneous melt mixtures containing succinonitrile (SCN) plasticizer and magnesium bis(trifluoromethane sulfonyl) imide Mg(TFSI)2 salt. The above solid-state Mg-PEM exhibits a Helmholtz electric double-layer capacitor (EDLC) behavior in its supercapacitive symmetric carbonaceous electrode configuration. The electrochemical stability for this PEM membrane (20/40/40 PEGDA/SCN/Mg (TFSI)2) was found to be approximately 3 V from linear sweep voltammetry with a specific capacitance of about 44 F/g from cyclic voltammetry and an energy density of approximately 17 Wh/kg in the 0–2 V range from the constant current density (CCD) experiment. Of particular interest is its excellent capacity retention of over 11,200 cycles, thus tested with the Coulombic efficiency of over 87%. Moreover, the energy density after extensive cycling for 11,200 has increased to approximately 56 Wh/kg at 10 mV/s in the potential range of 0–3 V relative to 17 Wh/kg in the potential range of 0–2 V at the same scan rate, attesting the excellent electrochemical stability and long life of the present Mg-PEM supercapacitor.