The present invention provides an electrolyte composition for a lithium or lithium-ion battery comprising a lithium salt in a liquid carrier comprising (a) a linear alkyl carbonate solvent, a cyclic alkyl carbonate solvent, or a combination thereof, and (b) a glycerol carbonate derivative compound of Formula (I):wherein X is selected from O, O(CO)O, S, N, P, P(═O), B, and Si; n is 1 when X is O, O(CO)O, or S; n is 2 when x is N, P, P(═O), or B; n is 3 when X is Si; and each R independently is selected from alkyl, alkenyl, alkynyl, aryl, acyl, heteroaryl, a 5-member ring heterocyclic group, a 5-member ring heterocycle-substituted methyl group, trialkylsilyl, and any of the foregoing substituted with one or more fluoro substituents, provided that R is acyl only when X is O, S, or N, and R is not alkyl when X is O(CO)O.