Three-dimensional graphene architectures in the macroworld can in principle maintain all the extraordinary nanoscale properties of individual graphene flakes. However, current 3D graphene products suffer from poor electrical conductivity, low surface area and insufficient mechanical strength/elasticity; the interconnected self-supported reproducible 3D graphenes remain unavailable. Here we report a sugar-blowing approach based on a polymeric predecessor to synthesize a 3D graphene bubble network. The bubble network consists of mono- or few-layered graphitic membranes that are tightly glued, rigidly fixed and spatially scaffolded by micrometre-scale graphitic struts. Such a topological configuration provides intimate structural interconnectivities, freeway for electron/phonon transports, huge accessible surface area, as well as robust mechanical properties. The graphene network thus overcomes the drawbacks of presently available 3D graphene products and opens up a wide horizon for diverse practical usages, for example, high-power high-energy electrochemical capacitors, as highlighted in this work.