The thermal conductivities of the natural gas hydrate core samples and the mud layer core samples, which were recovered from the sedimentary layers under sea bottom offshore Japan, were measured with hot-disc transient method at the higher-pressure conditions that imitates the actual original sedimentary layer under both gas-saturated and water-saturated condition. As a result, at the temperatures higher than melting point of ice, the thermal conductivity of natural gas hydrate sediment sample under water-saturated condition was very close to that with gas-saturated condition. It suggests that pore space of recovered hydrate sediment samples was already filled with water. Regarding to the temperature dependence, the thermal conductivity of natural hydrate core sample was decreased discontinuously around the melting point of ice and became much lower value than that at the sub-zero temperatures. It seamed because water in pore space of the sample sediment was melted around the temperature. On the other hands, the thermal conductivity of natural mud layer core sample wasn't changed so much with temperature from 263K to 283K. Calculations of thermal conductivity with some mixing models were also carried out to examine the applicability of those to the natural hydrate sediment samples.