We introduce a new microsimulation model built on household transport data to study the distributional effects of carbon-based fuel taxation of private road transport in Germany. Our data includes annual mileage at the car-level, the distinction between fuel types, as well as car-specific fuel consumption, allowing for a very detailed analysis. The model allows focusing on different types of households as well as identifying effect heterogeneity across the income distribution. We compare the recent fuel tax scheme with three policy reform scenarios to empirically test several hypotheses regarding distributional effects of carbon pricing. We find that the legal status quo of the fuel tax has overall regressive effects, with the tax on petrol acting regressive and the tax on diesel acting progressive. A transformation of the current tax into a revenue-neutral carbon-harmonised fuel tax yields a progressive distributional effect, while an introduction of a new carbon tax on transport fuels is neither clearly regressive nor progressive. Combining both tax schemes also has non-regressive effects. Our results suggest that policy makers face various options for pricing road transport greenhouse gas emissions without causing an overall disproportionate tax burden on low-income households.