The limiting ionic molar conductivity (lambda(infinity)) of an electrolyte solution depends on the self-diffusion coefficient (D-s) of the pure solvent when the temperature (T) changes. To study the D-s-dependence of lambda(infinity), we proposed a new empirical relation lambda(infinity) proportional to (D-s/T)(t), with a parameter t. The relation is applied to the lambda(infinity) and D-s of alkali, tetra-alkyl ammonium, and halogen ions in water or methanol. All ions except for tetra-alkyl ammonium ions in water exhibit excellent linear relationships in their lambda(infinity) proportional to (D-s/T)(t) plots, with t in the range from 0.88 to 1.26. This is the first report showing an affirmative linear correlation between lambda(infinity) and D-s. (C) 2018 Elsevier B.V. All rights reserved.