The five-storey building for Bicester, costing £6.6m, comes as part of a town centre regeneration project.
Plans for the centre include a new library, hotel and retail outlets, as well as office space and a restaurant.
The submitted plans come after an exhibition in January and feedback from the public. They will be discussed by councillors in May.
The earmarked site is on the Franklins Yard car park, facing the new Wesley Lane and Wesley Square.
The first floor would include the new Oxfordshire County Council Library and would also house the Bicester Historical Society.
If approved, work will start in July and be completed by summer 2015.
Plans for a multi-million pound community centre in north Oxfordshire have been submitted.