Carbon sheets with 3D architectures, large graphitic interlayer spacing, and high electrical conductivity are highly expected to be an ideal anode material for sodium-ion hybrid capacitors (SIHCs). Pursuing a simple synthesis methodology and advancing it from the laboratory to industry is of great importance. In this study, a new approach is presented to prepare 3D framework carbon (3DFC) with the above integrated advantages by a direct calcination of sodium citrate without aid of any additional carbon source, template, or catalyst. The first-principle calculations verify that the large interlayer spacing and the curvature structure of 3DFC facilitate the sodium ion insertion/extraction. As a consequence, the optimal 3DFC sample exhibits high reversible capacity as well as excellent rate and cycling performance. On this basis, a dual-carbon SIHC is fabricated by employing 3DFC as battery-type anode and 3DFC-derived nanoporous carbon as capacitor-type cathode. It is able to deliver high energy- and power-density feature as well as outstanding long-term cycling stability in the potential range of 0–4.0 V. This study may open an avenue for developing high-performance carbon electrode materials and pushes the practical applications of SIHCs a decisive step forward.