An apparatus for the thermal conductivity measurement of electrolyte solution was constructed using the coated transient hot wire method. Tantalum wire coated by anodization was used in order to prevent the direct contact between the metal wire and electrolyte solution. Temperature corrections for the coated wire were performed and the effect on the whole measurement was found to be less than 0.5 %. The constructed apparatus was used to measure the thermal conductivity of LiBr + 1,3-propanediol + water and LiBr + LiI + 1,3-propanediol + water at the several conditions. The overall uncertainty in the measurement was less than 1.5 %.