The membranes that accurately separate solutes with close molecular weights in harsh solvents are of crucial importance for the development of highly-precise organic solvent nanofiltration (OSN). The physicochemical structures of the membrane need to be rationally designed to achieve this goal, such as customized crosslinked networks, thickness, and pore size. Herein, we synthesize a type of covalent organic polymer (COP) nanofilms with tailor-made thickness and pore structure using a cyclic deposition strategy for precise molecular sieving. By elaborately designing monomer structures and controlling deposition cycle numbers, the COP nanofilms linked by robust β-ketoenamine blocks were endowed with sub-nanometer micropores and a linearly tunable thickness of 10-40 nm. The composite membranes integrating COP nanofilms exhibited adjustable solvent permeance. The membranes further demonstrated steep and finely-regulated rejection curves within the molecular weight range of 200 to 400 Da, where the difference value was as low as 40 Da. The efficient purification and concentration of the antibacterial drug and its intermediate was well achieved. Therefore, the exploited COP nanofilms markedly facilitate the application of microporous organic polymers for precise molecular separation in OSN.