Investigations leading to understanding and development of solid state rechargeable magnesium batteries are important in view of the fact that the Mg is free from hazards, it's stability is high and it's natural resources are abundant. A Mg2+ ion conducting gel polymer electrolyte (GPE) is investigated for a possible application in solid stale rechargeable Mg battery. The GPE consists of polyacrylonitrile, propylene carbonate, ethylene carbonate and magnesium trifluoromethane sulfonate (magnesium triflate). The composition is optimized in view of the minimum liquid constituents required for the gel formation and the maximum specific conductivity (sigma). The cr of the GPE follows Arrhenius behavior and the energy of activation for ionic conduction is in the range between 0.13 and 0.16 eV. The a.c, impedance data of Mg/GPE/Mg symmetrical cells are analyzed by fitting the data to an equivalent circuit. The values of interfacial resistance (R-i) of the Mg/GPE, which is contributed by surface film resistance (R-f) on the Mg and charge-transfer resistance (R-ct) of the electrochemical reaction are evaluated. The Ri decreases with an increase of cell temperature. On the other hand, it increases with the ageing lime of the cell at ambient temperature.