He was caught on CCTV in McColls on King Edwards Drive, at around 1.15pm on Thursday 26 September 2013.
It is believed the man placed two packets of cakes into a carrier bag before leaving the store without paying for them.
He is described as a white man, with a broad build, grey hair and a goatee beard. He was wearing a yellow t-shirt and blue jeans.
PC Emma Hayes, of Harrogate Safer Neighbourhood Team, said:
If you are the man caught on camera and you are not responsible for this theft, I urge you to 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.
Anyone who can assist officers to progress this enquiry should contact Harrogate police on 101, select option 2 and ask for Emma Hayes. Alternatively, information can be emailed to firstname.lastname@example.org
Or call Crimestoppers anonymously on 0800 555111, quoting reference number 12130167181.