A heat-conductive silicone rubber composite sheet having excellent electrical insulation properties, superior strength and flexibility, excellent interlayer adhesion, and particularly favorable thermal conductivity is provided. The composite sheet includes a laminated structure comprising an inner layer and a pair of outer layers laminated to both surfaces of the inner layer. The inner layer is an electrically insulating synthetic resin film layer having a thermal conductivity of not less than 0.3 W/mK, and the outer layers are silicone rubber layers formed by curing a composition including (a) an organopolysiloxane, (b) a curing agent, (c) a heat-conductive filler, and (d) a silicon compound-based adhesion promoter having at least one group selected from the group consisting of an epoxy group, alkoxy groups, a methyl group, a vinyl group, and a group represented by the formula Si-H.