The Grove Road store, which sells books and music accessories, has been trading in the town for around 30 years.
It was first owned by Graham and Sheila Harper and bought by Nigel and Heather, whose surname is also Harper, eight years ago.
After much deliberation the couple have decided to reduce their overheads by closing the shop and taking Internet and telephone sales from an office in Hailsham.
Heather said, "It has nothing to do with the credit crunch — independent bookshops are a declining market and are closing at a rate of knots.
"Amazon has taken most of our profits over the years.
"It is a great shame but we have to accept life is changing and the modern way to shop is on the Internet — we are all guilty of it in some way."
Heather and Nigel employ two full-time members of staff. One will work for the online bookshop in Hailsham but the other position will be made redundant.
Heather said, "This has not been an easy decision and it is a shame for the staff because they would have liked to have carried on in the same way.
"We are very grateful to our loyal customers who have supported us over the years and we are sad to close the shop."
Harpers Books and Music is popular with many local schools, businesses and choirs and Heather and Nigel hope they will continue to provide good service for their customers, despite having no retail outlet.
"Unlike Waterstones and some of the other major bookshops we have no boundaries on where we buy books so we can find out of print publications and rare books," said Heather.
The store has reduced its prices in a closing down sale and will shut later this month.
After the shop closes customers can order online at www.harpersbookshop.com or by calling 441048.
juliet.perry@trbeckett.co.uk