Some 24 jobs will be lost when the Liskeard store shuts on 28 October.
A spokesman said the company had invested significantly in the store over the last two years, but substantial investment by a nearby Co-op had led to an "ongoing negative effect on the profitability and sustainability of the store".
The Liskeard store was one of three former Somerfields acquired by Appleby Westward from The Co-operative Group in late 2009 to develop as Eurospar supermarkets. Its two other Eurospars at Keynsham and Minehead closed last year when they became consistently unprofitable. The closure comes as a Spar in Milford Haven was this week converted to Eurospar.
The refit has added 2,500 lines and is expected to increase turnover by 15%.