Agriculture is responsible for 17–35% of global anthropogenic greenhouse gas emissions with livestock production contributing by approximately 18–22% of global emissions. Due to high monitoring costs and low technical potential for emission reductions, a tax on consumption may be a more efficient policy instrument to decrease emissions from agriculture than a tax based directly on emissions from production. In this study, we look at the effect of internalising the social costs of greenhouse gas emissions through a tax based on CO2 equivalents for 23 different foods. Furthermore, we compare the loss in consumer surplus and the changed dietary composition for different taxation scenarios. In the most efficient scenario, we find a decrease in the carbon footprint from foods for an average household of 2.3–8.8% at a cost of 0.15–1.73 DKK per kg CO2 equivalent whereas the most effective scenario led to a decrease in the carbon footprint of 10.4–19.4%, but at a cost of 3.53–6.90 DKK per kg CO2 equivalent. The derived consequences for health show that scenarios where consumers are not compensated for the increase in taxation level lead to a decrease in the total daily amount of kJ consumed, whereas scenarios where the consumers are compensated lead to an increase. Most scenarios lead to a decrease in the consumption of saturated fat. Compensated scenarios leads to an increase in the consumption of added sugar, whereas uncompensated scenarios lead to almost no change or a decrease. Generally, the results show a low cost potential for using consumption taxes to promote climate friendly diets.