The thermal properties of insulation material are essential to develop a high-temperature superconducting (HTS) power cable to be operated at around liquid nitrogen temperature. Unlike metallic materials, nonmetallic materials have a high thermal resistance; therefore special attention needs to be paid to estimate heat flow correctly. Thus, we have developed a precise instrument for measuring the thermal conductivity of insulating materials over a temperature range from 40 K to near room temperature using a cryocooler. Firstly, the measurement of thermal conductivity for Teflon is carried out for accuracy confirmation. For a supplied heat flux, the temperature difference between warm and cold side is measured in steady state, from which the thermal conductivity of Teflon is calculated and compared with published result of NIST. In addition, the apparent thermal conductivity of Polypropylene laminated paper (PPLP) is presented and its temperature dependency is discussed.