The aluminum-nitride-based composite material according to the present invention is an aluminum-nitride-based composite material that is highly pure with the content ratios of transition metals, alkali metals, and boron, respectively as low as 1000 ppm or lower, has AlN and MgO constitutional phases, and additionally contains at least one selected from the group consisting of a rare earth metal oxide, a rare earth metal-aluminum complex oxide, an alkali earth metal-aluminum complex oxide, a rare earth metal oxyfluoride, calcium oxide, and calcium fluoride, wherein the heat conductivity is in the range of 40 to 150 W/mK, the thermal expansion coefficient is in the range of 7.3 to 8.4 ppm/° C., and the volume resistivity is 1×1014 Ω·cm or higher.