With respect to an addition-curable thermally conductive silicone composition in which a silver filler is blended, a catalyst having a specific structure and an organohydrogen polysiloxane having a specific structure are used for the purpose of extending the working life at room temperature, while maintaining the flexibility, so that a thermally conductive silicone composition which is able to have a good balance between flexibility after curing and storage stability in one pack, while having extremely low thermal resistance and excellent reliability is achieved.