Recent studies have identified many potential climate change impacts on bridges. Considering the sheer number of these potential impacts, how can a bridge owner prioritise which impacts to consider, and for which bridges? This paper proposes a risk-based multi-criteria decision analysis method for systematically addressing these two questions simultaneously. The proposed method can be used to address both extreme and non-extreme impacts as opposed to focussing solely on extreme impacts as has been done in previous prioritisation studies related to climate change risks. The proposed method is based on four main components of risk: hazard, impact, vulnerability and consequences. Several indices characterising these components are used to address the previous two questions. To reflect the uncertainty in the analysis, the different indices are assessed optimistically and pessimistically. Additionally, to ensure a more transparent decision-making process the inclusion of a strength of evidence assessment is also proposed. The applicability of the method is then demonstrated on three illustrative case studies for three different potential climate change impacts. It is concluded that the proposed method is both feasible and appropriately fulfils its purpose. Nevertheless, the proposed method should be more elaborately tested on practical bridge case studies to further establish its applicability.