Polymer electrolytes are considered potential key enablers for lithium-metal batteries due to their compatibility with the lithium-metal negative electrode. Herein, cross-linked self-standing single-ion conducting polymer electrolytes are obtained via a facile UV-initiated radical polymerization using pentaerythritol tetraacrylate as the cross-linker and lithium (3-methacryloyloxypropylsulfonyl)-(trifluoromethylsulfonyl)imide as the ionic functional group. Incorporating propylene carbonate as charge-transport supporting additive allowed for achieving single-ion conductivities of 0.21 mS cm$^{-1}$ at 20 °C and 0.40 mS cm$^{-1}$ at 40 °C, while maintaining a suitable electrochemical stability window for 4 V-class positive electrodes (cathodes). As a result, this single-ion polymer electrolyte featured good cycling stability and rate capability in Li||LiFePO$_{4}$ and Li||LiNi$_{0.6}$Mn$_{0.2}$Co$_{0.2}$O$_{2}$ cells. These results render this polymer electrolyte as potential alternative to liquid electrolytes for high-energy lithium-metal batteries.