A double-sided guarded hot plate apparatus (GHP) is specifically designed, fabricated, and constructed for the measurement of thermal conductivities of insulation specimens operated down to liquid nitrogen temperature (-196 °C), at different controlled pressures from 0.005 Pa to 0.105 MPa. The specimens placed in this apparatus are 300 mm in diameter at various thicknesses ranging from 4 mm to 40 mm. The apparatus is different from traditional GHP in terms of structure, supporting and heating method. The details of the design and construction of the hot plate, the cold plates, the suspensions, the clampings, and the vacuum chamber of the system are presented. The measurement methods of the temperatures, the input power, the meter area, and the thickness of the specimens are given. The apparatus is calibrated with teflon plates as sample and the maximum deviation from the published data is about 6% for thermal conductivity. The uncertainties for the measurement are also discussed in this paper.