In this study we synthesized the triazine-based two-dimensional covalent organic frameworks (COFs) TPTP-COF and TPDA-COF through Schiff base (imine) condensations of 2,4,6-tris(4-formylphenyl)-1,3,5-triazine (TPT-3CHO) with 2,4,6-tris(4-aminophenyl)triazine (TPT-3NH2) and diaminoanthraquinone (DAAQ), respectively. Moreover, we used carbon nanotube fibers (f-CNFs) as a template to synthesize TPTP-COF@f-CNF and TPDA-COF@f-CNF nanocomposite materials. X-ray diffraction image analysis revealed that our two COF materials possessed hexagonal crystal structures, with the crystallinity of TPTP-COF being much higher than that of TPDA-COF. Through simulations using Material Studio software, we determined an AA stacking structure for TPTP-COF and an AB stacking structure for TPDA-COF. These COF materials had high specific surface areas, charge transfer capability, and high redox properties, making them suitable for use in supercapacitor applications. TPTP-COF– and TPDA-COF–based electrodes provided specific capacitances of 577.4 and 640.4 F g−1, respectively, at a scan rate of 5 mV s−1. The specific capacitance of the TPTP-COF@f-CNF and TPDA-COF@f-CNF electrodes decreased upon increasing the f-CNF content. The maximum specific capacitances of TPTP-COF– and TPDA-COF–based symmetric supercapacitor devices were 56.4 and 70.6 F g−1, respectively. The TPTP-COF– and TPDA-COF–based devices both exhibited good electrochemical stability, preserving 78.60 and 81.54%, respectively, of their initial capacitances after 10,000 cycles. The energy density and power density of the TPDA-COF–based device were slightly better than those of the TPTP-COF–based device.