Due to strong van der Waals interactions, graphene nanosheets stack together, resulting in inefficient charge storage, which significantly compromises their performance as electrodes in supercapacitors. Herein, we design a hybrid material by interacting covalent organic frameworks (COFs) into reduced graphene oxide (rGO) films or fibers. The 2D COF nanosheets contain abundant mesopores, which prevents the stacking of rGO nanosheets, enabling the efficient electrolyte ion mass transfer. The optimal COF/rGO hybrid delivers a high gravimetric specific capacitance of 321 F g−1 and volumetric specific capacitance of 237 F cm−3 in an aqueous electrolyte measured in the three-electrode configuration, representing a breakthrough in capacitive graphene electrodes. Consequently, the fabricated 2D thin-film and 1D fiber supercapacitors deliver a high device energy density of 10.3 Wh kg−1 or 7.9 mWh cm−3 in aqueous and gel electrolytes, respectively. Moreover, an ultrahigh stack energy density of 87 Wh L−1 at the power density of 638 W L−1 is achieved using an ionic liquid electrolyte, which is superior to most of the carbon-based supercapacitors reported so far, as well as commercial lead-acid and lithium thin-film batteries. Overall, this study demonstrates 2D COFs as a critical enabler to realize high-performance graphene supercapacitors. 2D COFs also have the potential to enable unique architectures for many other 2D materials.