The revised hours, which reflect customer demand for key services of council tax, housing enquiries, benefits, will go before the City Council's Executive on Tuesday 4 February.
If the changes are accepted, the Customer Service Centre will open from 9am to 6pm on Mondays and Thursdays and 9am to 5pm on Tuesdays, Wednesdays and Fridays
Currently the Customer Service Centre opens from 8.30am to 5pm four days a week but stays open until 7pm on Thursdays.
Cllr Rob Hannaford, Lead Councillor for Housing and Customer Access, said the Council had been trialling the late night opening on Thursdays since March last year but it hadn't been very popular.
"We wanted to give people who work during the day greater opportunities for visiting the Council and at the same time support Exeter's late night economy by leading the way and encouraging other businesses to open up later in the evenings.
"Although some people have taken advantage of the later opening, the vast majority of people who visit the Civic Centre do so during more traditional hours, which is their choice entirely.
"Very few people attend before 9am but looking at those who visit after 5pm, we understand that their needs are best met by staying open until 6pm two days a week. We hope people will find these new hours useful and we will continue to review our opening hours to ensure they meet the needs of those who use it."
The Customer Service Centre deals with all City Council enquiries including council tax, housing enquiries, benefits and planning.
