Background: Reducing the alcohol-attributable cancer burden in the WHO European Region is a public health priority. This study aims to estimate the number of potentially avoidable cancers in countries of the WHO European Region in 2019 for three scenarios in which current excise duties on alcoholic beverages were increased by 20%, 50%, or 100%. Methods: Mean prices and excise duties for beer, wine, and spirits in the Member States of the WHO European Region in 2020 were used as the baseline scenario. We assumed that increases in excise duties (20%, 50%, and 100%) were fully incorporated into the consumer price. Beverage-specific price elasticities of demand, with lower elasticities for heavy drinkers, were obtained from a meta-analysis. Model estimates were applied to alcohol exposure data for 2009 and cancer incidence and mortality rates for 2019, assuming a 10-year lag time between alcohol intake and cancer development and mortality. Findings: Of 180,887 (95% Confidence interval [CI]: 160,595-201,705) new alcohol-attributable cancer cases and 85,130 (95% CI: 74,920-95,523) deaths in the WHO European Region in 2019, 5·9% (95% CI: 5·6-6·4) and 5·7% (95% CI: 5·4-6·1), respectively, could have been avoided by increasing excise duties by 100%. According to our model, alcohol-attributable female breast cancer and colorectal cancer contributed most to the avoidable cases and deaths. Interpretation: Doubling current alcohol excise duties could avoid just under 6% (or 10,700 cases and 4,850 deaths) of new alcohol-attributable cancers within the WHO European Region, particularly in Member States of the European Union where excise duties are in many cases very low. Funding: None.