A new steady-state apparatus is designed and constructed for the measurement of thermal conductivity (up to 25 W/mK) on a square specimen (300 mm side) with a heating temperature range from 30 °C to 900 °C. A vacuum container, of which the pressure can reach to 1 Pa, is also built for materials which can be easily oxidized. The structure of the facility is different from that of traditional steady-state devices, especially for the design of heating plate and heat sink. To verify the temperature uniformity of the heating plate, a simulation analysis is carried out in this paper. Besides, the heating system, the heat sink, the measuring system, and the vacuum system are presented in detail. In addition, the thermal conductivities of a heat insulation tile, 304L stainless steel, n-docosane, and erythritol are measured by this apparatus. Finally, an uncertainty analysis is discussed depending on different temperatures and materials.