NOVELTY - Rechargeable lithium cell comprises a cathode having a cathode active material, an anode having an anode active material, a porous separator electronically separating the anode and the cathode, and a non-flammable quasi-solid electrolyte in contact with the cathode and the anode. The electrolyte contains a lithium salt dissolved in a first organic liquid solvent with a concentration sufficiently high so that the electrolyte exhibits a vapor pressure less than 0.01 kPa when measured at 20 degrees C.    USE - The rechargeable lithium cell is useful as power source for electric vehicle (EV), hybrid electric vehicle (HEV), and portable electronic devices, such as lap-top computers and mobile phones.    ADVANTAGE - The rechargeable lithium cell is a lithium-air cell having a higher round-trip efficiency or higher resistance to capacity decay as compared to a corresponding lithium-air cell that has an electrolyte salt concentration lower than a molecular ratio of 0.2 (claimed). The battery cell is non-flammable and safe, and has a long cycle life, high capacity, high performance, and high energy density.    DETAILED DESCRIPTION - Rechargeable lithium cell comprises a cathode having a cathode active material, an anode having an anode active material, a porous separator electronically separating the anode and the cathode, and a non-flammable quasi-solid electrolyte in contact with the cathode and the anode, where the electrolyte contains a lithium salt dissolved in a first organic liquid solvent with a concentration sufficiently high so that the electrolyte exhibits a vapor pressure less than 0.01 kPa when measured at 20 degrees C, a vapor pressure less than 60% of the vapor pressure of the first organic solvent alone, a flash point at least 20 degrees C higher than a flash point of the first organic liquid solvent alone, a flash point higher than 150 degrees C, or no flash point, and the rechargeable lithium cell does not include a lithium-sulfur cell; or rechargeable lithium cell selected from a lithium metal secondary cell, a lithium-ion cell, a lithium-sulfur cell, a lithium-ion sulfur cell, or a lithium-air cell, comprises a cathode having a cathode active material, an anode having an anode active material, a porous separator separating the anode and the cathode, and a non-flammable quasi-solid electrolyte in contact with the cathode and the anode, where the electrolyte contains a lithium salt dissolved in a first organic liquid solvent with a concentration sufficiently high so that the electrolyte exhibits a vapor pressure less than 0.01 kPa when measured at 20 degrees C, a vapor pressure less than 60% of the vapor pressure of the first organic solvent alone, a flash point at least 20 degrees C higher than a flash point of the first organic liquid solvent alone, a flash point higher than 150 degrees C, or no flash point, where the lithium salt has a concentration greater than a molecular ratio of 0.2 and the lithium salt does not contain lithium trifluoromethanesulfonimide (LiTFSI) alone.