The composite silicone rubber sheet comprises a thermal conductive silicone rubber layer, both surfaces of which are tacky, containing a thermal conductive filler such as aluminum oxide and having a Asker C hardness of 5 to 50 and a thickness of 0.4 mm or less; at least one reinforcing sheet such as glass cloth arranged within said silicone rubber layer; and a releasable protective sheet such as a release paper covered on at least one tacky surface of said silicone rubber layer. Since the composite silicone rubber sheet is superior in thermal conductivity and has a good flexibility and tackiness, when used as a heat dissipating insulation sheet, the composite silicone rubber sheet has the advantages of being superior in adherence, free of oil-bleeding, suitable for mass-production, and capable of not lowering workability in assembling electronic parts and the like. The composite silicone rubber sheet is thin and lightweight and has a superior thermal conductivity, so that it can be used in the heat dissipation of a display panel for mounting on motor vehicles, railway vehicles or aircrafts.