To develop effective climate change policy, decision-makers need to have the best possible understanding of the available climate science. The IPCC Assessment Reports therefore aim to lay the foundation for informed political decision-making by providing policy-relevant information. But how successful are IPCC reports at communicating key findings? Although IPCC reports display key information in graphs, the interpretation of such graphs has received little attention. Here we provide an empirical evaluation of IPCC graph comprehension among IPCC target audience (N = 110), (political) decision-makers from climate-related (non-)governmental organizations from 54 countries, and a comparative sample of German junior diplomats, representing future international decision-makers (N = 33). We assess comprehension of current climate change risk visualizations using two IPCC graphs, one that employs principles of intuitive design, and one that violates principles of intuitive design. Results showed that (i) while a minority of IPCC target audience misinterpreted the intuitive graph, (ii) the majority of participants systematically misinterpreted the counter-intuitive graph, drawing the opposite conclusion from what was meant to be conveyed by the graph, despite (iii) having high confidence in the accuracy of their interpretation. Since misinterpretation of IPCC graphs does not allow for optimal use of the scientific information for policy-making, the results emphasize the importance of IPCC graphs that follow the principles of intuitive design.