This paper analyzes the extent to which the reduction of import tariffs ‒ as a measure of import competition ‒ affects the quality upgrading of the food products exported to the EU. This relationship is studied within a ‘distance to the frontier’ model (Aghion et al., 2005) who predicts a non-monotonic relation between competition and innovation. Quality is inferred from trade data using the Khandelwal (2010) method. The results show strong support for the existence of an non-monotonic relationship between competition and quality upgrading, with varieties close to the world frontier more likely to upgrade quality in response to an increase in import competition.