Electrospinning technology was used to co-dope hydrolyzed polyacrylonitrile (hPAN) and a metal-organic framework (MOF) material (Cu/ZIF-8) to form a composite nanofiber membrane, which was further pre-oxidized and carbonized to construct a nanocarbon fiber membrane-type carbon paper material with excellent flexibility and hydrophilicity. The results of X-ray diffractometry, scanning electron microscopy, contact angle meter, aperture analyzer and thermal gravimetric analyzer show that Cu-CNFs carbon paper has a gradient pore structure formed by the stacking of nanocarbon fibers and MOF defects. MOF is evenly distributed on the carbon fibers in a “beaded” manner; Cu-CNFs have high flexibility at a thickness of 115 μm; the initial contact angle of Cu-CNFs is 55°, indicating that it has good hydrophilicity and water permeability; Cu-CNFs can maintain good stability at 360 ℃. This work provides a new strategy for areas such as gas diffusion layers in fuel cells and electrodes in flow batteries.