Covalent organic frameworks (COFs) have emerged as promising electrode materials in flexible and wearable supercapacitors. However, achieving high electrical conductivity and high mechanical strength of flexible COF composite membranes is still a major challenge. Herein, we first prepared the COF complex by using hydroxyl-ended hyperbranched polymer (OHP) as a template via a simple solid-state mechanical mixing method, and the [email protected] complex was then impregnated on a microporous carbon nanotube film (CNTF) to construct a composite membrane (CHCM) that can be prepared as CHCM electrodes for extensible and flexible supercapacitors. A large number of cavities, reactive end-groups and flexible polymer chains of the hyperbranched polymer are utilized to stabilize and disperse COFs and to enhance the COF-polymer’s interfacial interaction. CNTF is an attractive material for energy storage due to its excellent conductivity, slippability, flexibility, and high specific surface area. The CHCM electrode showed not only excellent electrochemical performance (high gravimetric capacitance of 249 F g−1 and charging-discharging stability of 80% after 10,000 cycles) in the relatively environmentally-friendly phosphoric acid (H3PO4) electrolyte, but also a high tensile strength of 180 MPa and an elongation of 10%. The gravimetric capacitance of the CHCM electrode reached 425 F g−1 in 2 M aq. H2SO4 electrolyte. This work will demonstrate a promising strategy for preparing wearable and flexible supercapacitors with high mechanical strength with potentially wide applications.