Ambrosia artemisiifolia is an invasive weed in Europe with highly allergenic pollen. Populations are currently well established and cause significant health problems in the French Rhône valley, Austria, Hungary and Croatia but transient or casual introduced populations are also found in more Northern and Eastern European countries. A process-based model of weed growth, competition and population dynamics was used to predict the future potential for range expansion of A.artemisiifolia under climate change scenarios. The model predicted a northward shift in the available climatic niche for populations to establish and persist, creating a risk of increased health problems in countries including the UK and Denmark. This was accompanied by an increase in relative pollen production at the northern edge of its range. The southern European limit for A.artemisiifolia was not expected to change; populations continued to be limited by drought stress in Spain and Southern Italy. The process-based approach to modelling the impact of climate change on plant populations has the advantage over correlative species distribution models of being able to capture interactions of climate, land use and plant competition at the local scale. However, for this potential to be fully realised, additional empirical data are required on competitive dynamics of A.artemisiifolia in different crops and ruderal plant communities and its capacity to adapt to local conditions.