A heat-reducing silicone grease composition comprising a mixture of (A) 50-95 weight % of aluminum nitride powder having an average particle size of 0.5-10 &mgr;m and containing no particles 100 &mgr;m or greater in size, (B) 5-50 weight % of liquid silicone having a viscosity of 50-500,000 cs at 25° C. and (C) 0-30 weight % of at least one powder selected from the group consisting of zinc oxide, alumina, boron nitride and silicon carbide powders; and a semiconductor device to which the foregoing silicone grease composition is applied.