Capture of CO2 from the air offers a promising approach to addressing climate change and achieving carbon neutrality goals1,2. However, the development of a durable material with high capacity, fast kinetics and low regeneration temperature for CO2 capture, especially from the intricate and dynamic atmosphere, is still lacking. Here a porous, crystalline covalent organic framework (COF) with olefin linkages has been synthesized, structurally characterized and post-synthetically modified by the covalent attachment of amine initiators for producing polyamines within the pores. This COF (termed COF-999) can capture CO2 from open air. COF-999 has a capacity of 0.96 mmol g-1 under dry conditions and 2.05 mmol g-1 under 50% relative humidity, both from 400 ppm CO2. This COF was tested for more than 100 adsorption-desorption cycles in the open air of Berkeley, California, and found to fully retain its performance. COF-999 is an exceptional material for the capture of CO2 from open air as evidenced by its cycling stability, facile uptake of CO2 (reaches half capacity in 18.8 min) and low regeneration temperature (60 °C).