Owing to the limited reserves of fossil fuels, many researchers are focused on seeking advanced materials to relieve the drawbacks caused by the imbalance between the supply and demand of fossil fuels. In this study, a N, S co-doped graphene/multi-walled carbon nanotubes hybrid membrane (GMHE) was synthesized by flow-directed assembly followed by vapor-phase reduction. The resulting hybrid membrane not only exhibited excellent capacitance performance, but also good adsorption capacity for organic pollutants owing to its high electrochemical activity, well-developed pore structure, and rich surface state. The assembled GMHE all-solid-state symmetric supercapacitor delivered a high power density of 6000 W·kg−1 at an energy density of 16.0 W·h·kg−1 and superior capacitance stability (retaining 97.2 % of its initial capacitance value at 3 A·g−1). The adsorption capacity of the GMHE for organic pollutants was 50 times (chlorobenzene) its own mass. In addition, the hybrid membrane exhibited remarkable reusability over in adsorption–combustion cycles. The judiciously designed bifunctional membrane material developed herein can be directly applied in energy storage and oil pollution cleanup, supporting sustainable economic development.