Ionic liquids thermodynamically compatible with Li metal are very promising for applications to rechargeable lithium batteries. 1-methyl-3-propylpyrrolidinium bis(trifluoromethanesulfonyl)imide (P13TFSI) is screened out as a particularly promising ionic liquid in this study. Dimensionally stable, elastic, flexible, nonvolatile polymer gel electrolytes (PGEs) with high electrochemical stabilities, high ionic conductivities and other desirable properties have been synthesized by dissolving Li imide salt (LiTFSI) in P13TFSI ionic liquid and then mixing the electrolyte solution with poly(vinylidene-co-hexafluoropropylene) (PVDF-HFP) copolymer. Adding small amounts of ethylene carbonate to the polymer gel electrolytes dramatically improves the ionic conductivity, net Li ion transport concentration, and Li ion transport kinetics of these electrolytes. They are thus favorable and offer good prospects in the application to rechargeable Li batteries including open systems like Li/air batteries, as well as more "conventional" rechargeable lithium and lithium ion batteries.