Graphene and carbon nanotubes (CNTs) are attractive electrode materials for supercapacitors. However, challenges such as the substrate-limited growth of CNTs, nanotube bundling in liquid electrolytes, under-utilized basal planes, and stacking of graphene sheets have so far impeded their widespread application. Here we present a hybrid structure formed by the direct growth of CNTs onto vertical graphene nanosheets (VGNS). VGNS are fabricated by a green plasma-assisted method to break down and reconstruct a natural precursor into an ordered graphitic structure. The synergistic combination of CNTs and VGNS overcomes the challenges intrinsic to both materials. The resulting VGNS/CNTs hybrids show a high specific capacitance with good cycling stability. The charge storage is based mainly on the non-Faradaic mechanism. In addition, a series of optimization experiments were conducted to reveal the critical factors that are required to achieve the demonstrated high supercapacitor performance.