In this work, the thermal properties of a single-walled carbon nanotube (SWCNT) crystal are studied. The thermal conductivity of the SWCNT crystal is found to have a linear dependence on temperature in the temperature range from 1.9 K to 100.0 K. In addition, a peak (658 W/mK) is found at a temperature of about 100.0 K. The thermal conductivity decreases gradually to a value of 480 W/mK and keeps almost a constant in the temperature range from 100.0 K to 300.0 K. Meanwhile, the specific heat shows an obvious linear relationship with temperature in the temperature range from 1.9 K to 300.0 K. We discuss the possible mechanisms for these unique thermal properties of the single-walled carbon nanotube crystal.