Two-dimensional (2D) covalent organic framework (COF) materials have the most suitable microstructure for membrane applications in order to achieve both high flux and high selectivity. Here, we report the synthesis of a crystalline TFP-DHF 2D COF membrane constructed from two precursors of 1,3,5-triformylphloroglucinol (TFP) and 9,9-dihexylfluorene-2,7-diamine (DHF) through the Langmuir–Blodgett (LB) method, for the first time. A single COF layer is precisely four-unit-cell thick and can be transferred to different support surfaces layer-by-layer. The TFP-DHF 2D COF membrane supported on anodic aluminum oxide (AAO) porous supports displayed remarkable permeabilities for both polar and nonpolar organic solvents, which were approximately 100 times higher than that of the amorphous membranes prepared by the same procedure and similar to the best of the reported polymer membranes. The transport mechanism through the TFP-DHF 2D COF membrane was found to be a viscous flow coupled with a strong slip boundary enhancement, which was also different from those of the amorphous polymer membranes. The membrane exhibited a steep molecular sieving with a molecular weight retention onset of approximately 600 Da and a molecular weight cut-off of approximately 900 Da. The substantial performance enhancement was attributed to the structural change from an amorphous structure to a well-defined ordered porous structure, which clearly demonstrated the high potential for the application of 2D COFs as the next generation of membrane materials.