Abstract: Provided is a process for producing a ceramic for a heat-radiating member. The process includes providing as a raw material an alumina powder having an alumina (Al2O3) content of at least 99.5 mass % and an average particle size of from 0.2 to 1 ?m, and granulating the powder into a granular form ranging from 50 to 100 ?m, pressing the raw material which has been obtained in the granulation step and which includes granular alumina, and heating a green compact in an air atmosphere at a firing temperature of from 1,480 to 1,600° C. to obtain a sintered body. Also provided is a process for producing a ceramic for a heat-radiating member, the ceramic being a sintered alumina body which has high thermal conductivity, efficient heat dissipation, excellent mechanical strength and thermal shock resistance and which is usable for cooling applications at heat generating areas of electronic devices and equipment.