By adopting results from past research concerning the freezing phenomenon of supercooled water and the method to control the initiation of the freezing, a method for measuring thermal conductivity of water below the freezing temperature was introduced. The method was basically a non-steady-state hot-wire method, and a few modifications were made to avoid freezing during the measurement. It was found that the thermal conductivity of supercooled water can be measured by considering factors such as selection of vessel material, size and shape, reduction of the complexity of the whole instrument, and purity of water. Consequently, thermal conductivity was obtained at 265K. According to the results obtained, the thermal conductivity decreases gradually with decreasing temperature, and follows a tendency similar to the temperature dependence at the region higher than the freezing point.