Developing effective synthetic strategies as well as enriching functionalities for sp2 -carbon-linked covalent organic frameworks (COFs) still remains a challenge. Now, taking advantage of a variant of Knoevenagel condensation, a new fully conjugated COF (g-C34 N6 -COF) linked by unsubstituted C=C bonds was synthesized. Integrating 3,5-dicyano-2,4,6-trimethylpyridine and 1,3,5-triazine units into the molecular framework leads to the enhanced π-electron communication and electrochemical activity. This COF shows uniform nanofibrous morphology. By assembling it with carbon nanotubes, a flexible thin-film electrode for a micro-supercapacitor (MSC) can be easily obtained. The resultant COF-based MSC shows an areal capacitance of up to 15.2 mF cm-2 , a high energy density of up to 7.3 mWh cm-3 , and remarkable rate capability. These values are among the highest for state-of-the-art MSCs. Moreover, this device exhibits excellent flexibility and integration capability.