The effect of the lithium perchlorate concentration in sulfolane (in the range from 0.1M to 2.8М) on the performance of lithium-sulfur cells is studied. It is shown that the concentration of lithium perchlorate in sulfolane considerably affects the depth of electrochemical reduction of sulfur, the reactivity of lithium polysulfides, and the coulomb efficiency of cycling of lithium-sulfur cells. The maximum depth of electrochemical reduction of sulfur is reached at the concentration of lithium perchlorate in sulfolane of 1.0M, while the minimum depth is reached at 2.8М. The depth of electrochemical reduction of sulfur is limited by the number of free solvent molecules. An increase in the concentration of the support salt results in an increase in the coulomb efficiency of cycling of lithium-sulfur cells. At concentrations of the support salt above 2.4М, the coulomb efficiency of cycling of lithium-sulfur cells is close to 100%. We believe that the concentration of support salts affects the species of lithium polysulfides, their association-dissociation equilibria in electrolyte solutions and the processes of solvation of lithium ions contained in lithium polysulfides and support salts, and thus determines the performance of lithium-sulfur cells.