A thermally conductive silicone grease composition comprising: (A) an organopolysiloxane having at least two alkenyl groups in one molecule and having a kinetic viscosity of 5,000 to 100,000 mm2/s at 25° C.; (B) a hydrolyzable methylpolysiloxane having a trifunctional termination at one end and represented by the following general formula (2): wherein R2 represents an alkyl group having 1 to 6 carbon atoms and b is an integer of 5 to 100; (C) a thermally conductive filler having a thermal conductivity of at least 10 W/m·° C.; (D) an organohydrogenpolysiloxane containing from 2 to 5 hydrogen atoms in one molecule directly bound to silicon atoms (Si—H groups); (E) a bonding aid having a triazine ring and at least one alkenyl group in one molecule; and (F) a catalyst selected from the group consisting of platinum and platinum compounds.