The Barclays branch in North Hykeham in The Forum will close.
The bank announced last week that it will occupy a unit instead within Asda at North Hykeham from March 2014.
The Forum branch will close on Friday March 7 and the new branch in Asda will open on Monday March 10 2014.
The idea is to make banking more accessible and flexible to customers with busy lives.
Barclays current account customers will be able to use the Post Office in the Forum as part of reciprocal arrangement for services.
North Hykeham has been chosen as one of just eight pilots for the scheme across the UK.
The new Barclays will be open seven days a week and its opening hours will mirror the supermarket's.
Banking services will be available for longer than a high-street branch and there will be ample parking.
All new and existing Barclays customers will be able to use the new facility, which will be staffed during opening hours.
Outside of these hours, new technology will enable people tout transactions such as paying bills and transferring money.