It was stolen from a woman in Sainsburys, Wetherby Road, on Monday 24 June 2013.
The purse contained money and credit cards.
One of the cards was later used to purchase an Apple Mac Pro.
The suspect is described as a white man with a medium build and short hair.
PC Andy Hanson, of Harrogate Safer Neighbourhood Team, said:
If you are the man caught on CCTV and you are not responsible for this theft, please come forward and contact the police straight away, so that I can eliminate you from my enquiries.
I am also keen to speak to anyone who recognises the man and ask them to get in touch as soon as possible.
Anyone who can help officers with this enquiry should contact Harrogate police on 101, select option 2 and ask for Andy Hanson. Alternatively information can be emailed to firstname.lastname@example.org
Or call Crimestoppers anonymously on 0800 555 111 quoting reference number 12130103270.