A silicone grease composition having high thermal conductivity, comprising (A) 50 to 95 weight % of a mixture of an aluminum nitride powder &agr; having an average particle size of 0.5 to 5 &mgr;m and an aluminum nitride powder &bgr; having an average particle size of 6 to 20 &mgr;m, wherein the aluminum nitride powders &agr; and &bgr; are mixed so that the &agr;/(&agr;+&bgr;) ratio by weight is from 0.1 to 0.9 and the average particle size after mixing is from 1 to 10 &mgr;m, (B) 5 to 15 weight % of organopolysiloxanes having a viscosity of from 50 to 50,000 cs at 25° C. and represented by formula R1aSiO(4−a)/2, wherein R1 represents at least one group selected from saturated or unsaturated univalent hydrocarbon groups containing 1 to 18 carbon atoms and 1.8≦a≦2.2, and (C) 0 to 35 weight % of at least one inorganic compound powder having an average particle size of 0.5 to 100 &mgr;m selected from the group consisting of zinc oxide, alumina, boron nitride and silicon carbide powders.