The suspect was captured on CCTV at Tesco on Broughton Road at around 10am on Wednesday 19 January.
He used the cash machine outside the store to obtain £600, using a card he had stolen from his victim in Morrisons, a short time earlier.
The victim, a 69-year-old local woman, was shopping in Morrisons, when her purse containing, cash, cards and PIN numbers was taken from her bag at around 9.50am.
The suspect left the store and used her card to make two transactions of £300.
Police investigating the theft are urging the public to help them identify the man responsible. He is described as white, aged between 40 and 50-years-old, with a stocky build and short dark hair.
He was wearing a dark jacket with a grey panel across the back, dark trousers and black shoes.
PC Chris Dyson, of Skipton police, said:
“This was a disgraceful, thoughtless crime which was obviously very upsetting for the elderly victim.
“The CCTV image clearly shows the suspect and I would urge anyone who recognises him to contact the police or crimestoppers and tell us who he is. “I would also like to urge shoppers to take extra care of their belongings and follow the advice on the North Yorkshire Police website about protecting your personal belongings from thieves.”
Anyone with any information that could help the police with their enquiries is urged to contact PC Chris Dyson, of Skipton Police, on 0845 60 60 24 7, quoting reference number 12110009831.
Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111. More information about guarding against purse thefts can be found on the North Yorkshire Police website www.northyorkshire.police.uk/pursethefts