The Co-op store on Hyde Road in Stratton St Margaret has been given a closing date.
The last day shoppers will be able to visit the store is November 23.
READ: All of Swindon's store closures in 2019
The store is one of three within a mile of each other but is the biggest.
The closure will put 17 jobs at risk.
A spokesman for Co-op said: "Co-op is moving forward with real purpose and momentum, and while this usually involves the opening of new stores, we also have to make difficult decisions.
"After careful consideration, our store in Stratton St Margaret will close.
"The last day of trading is expected to be November 23.
"This is no way a reflection of the hard work of colleagues, who have been informed, and every effort will be made to find alternative roles for them.
"We would like to thank the community for its support over the years."
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