A liquid catholyte for a Li—S battery comprises a non-aqueous solution of at least one lithium polysulfide of formula Li2Sx (wherein x is selected from 4, 6, and 8) and an anion receptor compound capable of complexing with polysulfide anion. The non-aqueous solution typically is composed of the Li2Sx and the anion receptor compound dissolved in a non-aqueous solvent (e.g., one or more organic ether or fluorinated ether solvents). The anion receptor compound typically is present in the catholyte at a concentration of about 0.1 M to about 4 M. Li—S batteries comprise a metallic lithium anode; a porous conductive substrate; a separator membrane between the anode and the porous conductive substrate; and the liquid catholyte composition within pores of the substrate.