1. Effective prevention and control of invasive species generally relies on a comprehensive, coherent and representative list of species that enables resources to be used optimally. European Union (EU) Regulation 1143/2014 on invasive alien species (IAS) aims to control or eradicate priority species, and to manage pathways to prevent the introduction and establishment of new IAS; it applies to species considered of Union concern and subject to formal risk assessment. So far, 49 species have been listed but the criteria for selecting species for risk assessment have not been disclosed and were probably unsystematic. 2. We developed a simple method to systematically rank invasive alien species according to their maximum potential threat to biodiversity in the EU. We identified 1323 species as potential candidates for listing, and evaluated them against their invasion stages and reported impacts, using information from databases and scientific literature. 3. 900 species fitted the criteria for listing according to IAS Regulation. We prioritised 207 species for urgent risk assessment, 59 by 2018 and 148 by 2020, based on their potential to permanently damage native species or ecosystems; another 336 species were identified for a second phase (by 2025), to prevent or reverse their profound impacts on biodiversity; and a further 357 species for assessment by 2030. 4. Policy implications. We propose a systematic, proactive approach to selecting and prioritising invasive alien species for risk assessment to assist European Union policy implementation. We assess an unprecedented number of species with potential to harm EU biodiversity using simple methodology that we developed, and recommend which species should be considered for risk assessment in a ranked order of priority along the timeline 2018-2030, based on their maximum reported impact and their invasion history in Europe.