With increased energy density of rechargeable lithium-ion batteries for powering smart phones and electric vehicles and for their long range use, battery safety becomes more important than ever. This aspect motivated us to develop non-flammable liquid electrolyte that removes the risk of battery fire and explosion, which is urgently needed. Battery energy density and performance however should not be sacrificed to achieve just the safety. Here we report for the first time a rational design of non-flammable carbonate-based organic liquid electrolyte to satisfy safety, energy density and performance simultaneously. Our novel electrolyte, composed of 1 M lithium hexafluorophosphate salt and propylene carbonate and fluorinated linear carbonate co-solvents, at unmeasurable flash point does not fire representing non-flammable safe batteries but permits high-voltage stability to enable high-voltage charge of lithium-rich layered oxide cathode up to 5.0 V, high-energy density of 856 Wh per kg of cathode active mass and stable charge-discharge cycling performance of full-cell with graphite anode, in contrast to rapid performance fade of flammable conventional electrolyte system. The discovery of non-flammable carbonate-based organic liquid electrolyte opens up a new avenue to high-safety and high energy-density lithium-ion batteries for electric vehicles and advanced energy-storage applications.