The lack of access to clean water for billions of people represents a fundamental global sustainability challenge that must be addressed. Seawater desalination using membrane technologies provides a promising solution; however, the dominating desalination membranes often show low permeation flux and deficient fouling resistance. Here we achieve ultrafast desalination by taking advantage of covalent organic framework (COF) membranes where TaPa-SO3H nanosheets are linked by TpTTPA nanoribbons through electrostatic and π–π interactions to form an ordered and robust structure. The optimum COF membrane exhibits excellent rejection of NaCl (99.91%) and more importantly an ultrafast water flux of 267 kg m−2 h−1, which outperforms the state-of-the-art designs and is 4–10 times higher than conventional membranes. Furthermore, the desired fouling resistance underpins superior operational stability (108 h) and high salinity (7.5 wt%) tolerance, offering great potential in practical applications.