Provided is a heat conductive silicone grease composition, including: (A) 100 parts by volume of an organopolysiloxane with a specific structure and with a kinematic viscosity at 25° C. of 10 to 10,000 mm2/s, (B) 0.1 to 50 parts by volume of an alkoxysilane with a specific structure, and (C) 100 to 2,500 parts by volume of a heat conductive filler. The composition exhibits high thermal conductivity, retains excellent fluidity meaning the composition exhibits favorable workability, and is capable of filling fine indentations, thereby reducing contact resistance and providing excellent heat radiation performance. Also, the durability, under conditions of high temperature and high humidity, of the composition is improved, thereby improving the reliability of the composition during actual use. Heat generated by a heat-generating body can be dissipated into a heat-radiating body by sandwiching the composition between the heat-generating body and the heat-radiating body.