Officers say two men entered the former Somerfield store and attempted to buy two store vouchers for £400.
When their credit card was refused, one of the men grabbed the vouchers and made off.
A spokesman told Burnham-On-Sea.com: “We are trying to trace two men whom we think may be able to help with our enquiries into a case of fraud and theft which occurred at a supermarket in Highbridge on 20 July.”
Anyone with any information regarding the case should contact Crimestoppers on 0800 555 111 quoting case reference EM215_10.