A simulation model of international tourist flows is used to estimate the impact of a carbon tax on aviation fuel. The effect of the tax on travel behaviour is small: a global $1000/tC would change travel behaviour to reduce carbon dioxide emissions from international aviation by 0.8%. This is because the imposed tax is probably small relative to the air fare. A $1000/tC tax would less than double air fares, and have a smaller impact on the total cost of the holiday. In addition, the price elasticity is low. A carbon tax on aviation fuel would particularly affect long-haul flights, because of high emissions, and short-haul flights, because of the emission during take-off and landing. Medium distance flights would be affected least. This implies that tourist destinations that rely heavily on short-haul flights (that is, islands near continents, such as Ireland) or on intercontinental flights (e.g., Africa) will see a decline in international tourism numbers, while other destinations may see international arrivals rise. If the tax is only applied to the European Union, EU tourists would stay closer to home so that EU tourism would grow at the expense of other destinations. Sensitivity analyses reveal that the qualitative insights are robust. A carbon tax on aviation fuel would have little effect on international tourism, and little effect on emissions.