Solid-state magnesium (Mg) batteries have been constructed with a novel polymeric electrolyte that conducts Mg2+ ion at ambient temperature. The polymeric electrolyte consisting of oligo(ethylene oxide)-grafted polymethacrylate and a linear polyether dissolving an Mg salt showed as high ionic conductivity as 0.4 mS cm(-1) at 60 degreesC. A test cell made of a V2O5 cathode and an Mg metal anode (Mg/V2O5) with the Mg2+-conducting polymeric electrolyte showed the first discharge capacity of about 100 mAh g (V2O5)(-1). The discharge capacity and the rechargeability of the cell were improved when Mg metal was substituted by Li metal. The discharge and recharge profile of the cell using an Mg-doped V2O5 anode (MgxV2O5/V2O5) proved that the present polymeric Mg2+-ion conductor will help to develop an all-solid rechargeable Mg-ion battery.