Robust tools are needed to prioritise the management of invasive non-native species (INNS). Risk assessment is commonly used to prioritise INNS, but fails to take into account the feasibility of management. Risk management provides a structured evaluation of management options, but has received little attention to date. We present a risk management scheme to assess the feasibility of eradicating INNS that can be used, in conjunction with existing risk assessment schemes, to support prioritisation. The Non-Native Risk Management scheme (NNRM) can be applied to any predefined area and any taxa. It uses semi-quantitative response and confidence scores to assess seven key criteria: Effectiveness, Practicality, Cost, Impact, Acceptability, Window of opportunity and Likelihood of re-invasion. Scores are elicited using expert judgement, supported by available evidence, and consensus-building methods. We applied the NNRM to forty-one INNS that threaten Great Britain (GB). Thirty-three experts provided scores, with overall feasibility of eradication assessed as ‘very high’ (8 species), ‘high’ (6), ‘medium’ (8), ‘low’ (10) and ‘very low’ (9). The feasibility of eradicating terrestrial species was higher than aquatic species. Lotic freshwater and marine species scored particularly low. Combining risk management and existing risk assessment scores identified six established species as priorities for eradication. A further six species that are not yet established were identified as priorities for eradication on arrival as part of contingency planning. The NNRM is one of the first INNS risk management schemes that can be used with existing risk assessments to prioritise INNS eradication in any area.