Preventing the stacking of graphene is essential to exploiting its full potential in energy-storage applications. The introduction of spacers into graphene layers always results in a change in the intrinsic properties of graphene and/or induces complexity at the interfaces. Here we show the synthesis of an intrinsically unstacked double-layer templated graphene via template-directed chemical vapour deposition. The as-obtained graphene is composed of two unstacked graphene layers separated by a large amount of mesosized protuberances and can be used for high-power lithium-sulphur batteries with excellent high-rate performance. Even after 1,000 cycles, high reversible capacities of ca. 530 mA h g(-1) and 380 mA h g(-1) are retained at 5 C and 10 C, respectively. This type of double-layer graphene is expected to be an important platform that will enable the investigation of stabilized three-dimensional topological porous systems and demonstrate the potential of unstacked graphene materials for advanced energy storage, environmental protection, nanocomposite and healthcare applications.