Officers say he changed his clothing between the two visits to the Co-op store on Broadway, Fulford.
Altogether, he stole £800 of alcohol. The raids happened shortly before 1pm on January 13.
Police say if anyone recognises the man in the picture they should contact them as they believe he can help them in their investigation.
Anyone with any information is asked to email hazel.simms@northyorkshire.police.uk or call North Yorkshire Police on 101, select option 2 and ask for PC1338 Simms-Williamson.
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111. Please quote reference number 12240007528 when passing on information.
