Hastings Borough Council leader, Jeremy Birch, wants it introduced to mark the date of the Battle of Hastings in 1066.
The call comes after ministers outlined plans to scrap the May Day bank holiday and move it to St George's Day in April or Trafalgar Day in October.
Mr Birch wants the new holiday in addition to May Day as it is the date of the town's biggest festival.
He has written to Tourism Minister John Penrose explaining that the Jack-in-the Green event on the May Day bank holiday, which celebrates morris dancing, is very important because it attracts 20,000 people and generates Â£5m for businesses.
He said: "Our visitor economy would suffer greatly if the May Day bank holiday were to be moved, as he suggested.
"That doesn't mean that we wouldn't welcome another late season holiday and I have suggested 14 October for that.
"I told the minister that the date is known locally as Hastings Day - already the date of the fateful Battle of Hastings in 1066."
The proposal to move the May Day bank holiday is part of the the Department of Culture, Media  and Sport's (DCMS) tourism policy.
It is hoped it would lengthen the tourist season and attract more visitors to the UK.
The DCMS said it was consulting on the plans.
In a statement it said: "Some suggestions include creating a new St George's Day holiday in England, or a UK Day bank holiday in the autumn half term.
"However the consultation will allow new suggestions to be made."
Calls have been made for a new bank holiday to be introduced on 14 October called Hastings Day.