If adaptive evolution cannot keep up with rapid climate change, populations and even species may decline or go extinct. Such adaptational lag is predicted, but evidence is scarce. We tested for lagging adaptation to warming climate in banked seeds of the annual weed Arabidopsis thaliana in common garden experiments in four sites across the species’ native European climate range. Genotypes originating in climates historically warmer than the planting site had higher relative fitness than native genotypes in every site. This result suggests that local adaptive optima have shifted rapidly with recent climate warming across the species’ native range, and that the potential for adaptational lag deserves consideration in conservation and management decisions for many species.