A thermally conductive silicone grease composition comprising at least the following components: an organopolysiloxane (A) represented by the following general formula: [wherein R1 designates identical or different univalent hydrocarbon groups; X designates identical or different univalent hydrocarbon groups or alkoxysilyl-containing groups of the following general formula: —R2—SiR1a(OR3)(3-a) (wherein R1 designates the previously mentioned groups; R2 designates oxygen atoms or alkylene groups; R3 designates alkyl groups; and ‘a’ is an integer ranging from 0 to 2); and ‘m’ and ‘n’ are integers equal to or greater than 0, respectively]; a thermally conductive filler (B); and an organopolysiloxane (C) having silicon-bonded hydrogen atoms on both molecular terminals and in the molecular chains; is characterized by excellent resistance to heat and reduced oil bleeding.