A nanocomposite of metal-organic frameworks (MOFs)-HKUST-1 based on graphene oxide (GO) was modified by polydopamine (PDA). These nanomaterials formed the PDA/RGO/HKUST-1 membrane over the surface of the commercial cellulose acetate membrane support layer to treat dye wastewater. The membranes were characterized by Fourier transform infrared spectroscopy, scanning electron microscopy, atomic force microscopy, X-ray diffraction, and X-ray photoelectron spectroscopy. The results showed enhanced membrane separation performance because of improved surface flatness and layer spacing. With the insertion of porous HKUST-1 and the cross-linking modification of PDA, the PDA/RGO/HKUST-1 membranes exhibited excellent flux, rejection, hydrophilic, and anti-fouling performance. The composite membrane could effectively reject methylene blue and Congo red, with removal rates of 99.8% and 89.2%, respectively. In addition, the flux of the PDA/RGO/HKUST-1 membrane increased 31-fold with the addition of HKUST-1 and PDA. Overall, the prepared high-flux composite membrane can be used as an excellent material in a variety of environmental applications.