Graphene is known for its high surface‐area‐to‐mass ratio. However, for graphene to be used in engineering processes such as catalytic reactors or heat exchangers, high surface‐area‐to‐volume ratio is essential. Currently, graphene is only prepared in sheet form, which limits its surface‐area‐to‐volume ratio to around 200 m2 m−3. In this study, we propose and demonstrate a technique based on chemical vapour deposition (CVD) to realise graphene on a copper‐based micro‐tubular substrate to not only substantially increase its surface‐area‐to‐volume ratio to a value over 2000 m2 m−3, but also to eliminate maldistribution of flows commonly unavoidable in flat‐sheet configurations. Our approach uses a dual‐layer micro‐tubular substrate fabricated by a phase‐inversion facilitated co‐extrusion technique. In the substrate, a thin copper outer layer is employed to enable the CVD growth of graphene, and an inner Cu‐Fe layer is adopted to provide a strong mechanical support. Our study shows that this approach is feasible to produce graphene with a very high surface‐area‐to‐volume ratio for possible practical applications in catalytic reactors or heat exchangers, though problems such as the inter‐diffusion between the two metal layers and defects in graphene need to be further addressed. To the best of our knowledge, this study is the first attempt to prepare graphene with high surface‐area‐to‐volume ratio by a CVD route.