A heat dissipating silicone grease composition comprising: (A) 3% to 30% by weight of an organo polysiloxane represented by the general formula, R1aSiO(4−a)/2(R1 is one or two or more groups selected from a group of saturated or unsaturated monovalent hydrocarbon groups containing one to eighteen carbon atoms, and a is a positive number defined by 1.8≦a≦2.2) having a dynamic viscosity at 25° C. of 50 mm2/s to 500,000 mm2/s; (B) 60% to 96.9% by weight of a thermally conductive filler having a thermal conductivity of at least 10 W/(m·K); and (C) 0.1% to 10% by weight of a solvent that disperses or dissolves component (A).