Organic solvent nanofiltration (OSN) has become increasingly important in petrochemical and pharmaceutical industries, demanding superior and robust membranes. 2D MOF nanosheets hold great promise in the preparation of OSN membrane. Nevertheless, the fabrication of defect-free 2D MOF membranes with robust mechanical strength is hampered due to the weak interlamellar interactions between MOF nanosheets. Herein, 2D MOF composite membrane for high-performance OSN application is fabricated through the assembly of copper 1,4-benzene dicarboxylate (CuBDC) nanosheets and NH2-SWCNTs. Within this composite configuration, NH2-SWCNTs can shelter the defects between the adjacent CuBDC nanosheets, rendering CuBDC/CNTs composite membranes precise molecular sieving ability. Meanwhile, the nanochannels created by NH2-SWCNTs with low frictional coefficients on the internal surface promote the permeation of organic solvents. Moreover, the multiple interactions between CuBDC and NH2-SWCNTs improve the mechanical strength of composite membranes. Accordingly, the composite membranes display excellent rejections of dye molecules on the basis of size-sieving mechanism with superior methanol permeance of 1260 L m−2h−1 bar−1, as well as steady congo red rejection at high trans-membrane pressure of 5 bar, demonstrating good pressure resistance of composite membranes. Moreover, the composite membranes exhibit outstanding stability against high-concentration feeds and long-term operation for 50 h, confirming excellent practicality in the purification of dyes from organic solvents. The design approach in this work may inspire the fabrication of other nanosheet-based membranes for high-efficient OSN.