The WHO (World Health Organization) regards overweight and obesity as one of the major worldwide public health concerns. In France, according to the National Individual Survey on Food Consumers(INCA2 2006-2007), 38.9 % of men and 24.2 % of women are overweight and 11.6 % of men and women are obese. In 2002, according to the French Institute of Research in Health Economics (IRDES), the medical cost of obesity was estimated at between 1.5 and 4.6 % of health expenditure. The spread of obesity and its economic consequences led public authorities to think about measures to modify food consumption behaviours. By estimating a demand system, we assess the effect and relevance of a tax policy on food with high calories, fat and sugar content, called a “fat tax”. We show that the impact of this “fat tax” on purchases of food, nutrients and calories is weak. Its impact on body weight is also weak in the short run, but tends to increase in the long run. Lastly, while the “fat tax” generates high tax revenues, it mainly affects modest households.