The Panel on Plant Health performed a pest categorisation of the weevil Anthonomus quadrigibbus Say, (Coleoptera: Curculionidae), for the EU. A. quadrigibbus is a well‐defined and distinguishable species, recognised as an occasional pest of apples, pears and sour cherries in North America where it also feeds on a range of wild rosaceous plants such as Crataegus and Amelanchier. Adults feed on leaves, flowers and fruit. Feeding damage to fruit reduces quality. Females oviposit into young fruit, causing surface blemishes and resulting in distortion as the fruit develops. Marketability is subsequently reduced. Larvae and pupae develop within host fruit. Most infested fruit fall prematurely, reducing yield. A. quadrigibbus was regarded as a more serious pest in the early 20th century. A. quadrigibbus is not known to occur in the EU and is listed in Annex IIAI of Council Directive 2000/29/ EC under the synonym Tachypterellus quadrigibbus. Host plants for planting and infested fruit could potentially provide a pathway into the EU. Considering the climatic similarities between North America and Europe, and that wild and commercial hosts occur widely within the EU, A. quadrigibbus has the potential to establish within the EU. There would be one generation per year, as in North America. Impacts could be expected in apple, pear and perhaps sour cherry orchards. The level of impacts would be uncertain. There is also uncertainty regarding whether A. quadrigibbus would extend its host range to include other Rosaceae within the EU. Phytosanitary measures are available to reduce the likelihood of introduction of A. quadrigibbus. All criteria assessed by EFSA for consideration as a potential Union quarantine pest are met. As A. quadrigibbus is not known to occur in the EU, this criterion assessed by EFSA to consider it as a Union regulated non‐quarantine pest is not met.