Bioenergy with carbon capture and storage (BECCS) is recognized as a potential negative emission technology, needed to keep global warming within safe limits. With current technologies, large-scale implementation of BECCS would compromise food production. Bioenergy derived from phototrophic microorganisms, with direct capture of CO2 from air, could overcome this challenge and become a sustainable way to realize BECCS. Here we present an alkaline capture and conversion system that combines high atmospheric CO2 transfer rates with high and robust phototrophic biomass productivity (15.2 +/- 1.0 g/m(2)/d). The system is based on a cyanobacterial consortium, that grows at high alkalinity (0.5 mol/L) and a pH swing between 10.4 and 11.2 during growth and harvest cycles.