Carbon materials have been the most common anodes for sodium-ion storage. However, it is well-known that most carbon materials cannot obtain a satisfactory rate performance because of the sluggish kinetics of large-sized sodium-ion intercalation in ordered carbon layers. Here, we propose an integration of co-intercalation and adsorption instead of conventional simplex-intercalation and adsorption to promote the rate capability of sodium-ion storage in carbon materials. The experiment was demonstrated by using a typical carbon material, reduced graphite oxide (RGO400) in an ether-solvent electrolyte. The ordered and disordered carbon layers efficiently store solvated sodium ions and simplex sodium ions, which endows RGO400 with enhanced reversible capacity (403 mA h g -1 at 50 mA g -1 after 100 cycles) and superior rate performance (166 mA h g -1 at 20 A g -1 ). Furthermore, a symmetric sodium-ion capacitor was demonstrated by employing RGO400 as both the anode and cathode. It exhibits a high energy density of 48 W h g -1 at a very high power density of 10,896 W kg -1 . This work updates the sodium-ion storage mechanism and provides a rational strategy to realize high rate capability for carbon electrode materials.