The candidate will be David Furness, the party's organiser in west London, who stood in the 2011 Feltham and Heston Parliamentary by-election.
A spokesman for the BNP told BBC London the party had been "rebuilding and modernising" since May.
The BNP fielded eight candidates at the general election.
A BNP spokesman said the party was not worried about lack of resources: "We didn't bankrupt ourselves by standing in too many seats in May, unlike UKIP."
Reports to the Electoral Commission show it had a total income of more than Â£600,000 in 2013, the latest year for which complete figures are available, down from more than Â£1.2m in 2010.
He said the party had been "rebuilding and modernising through the support of our members after a recent scaling-down in activity".
In 2012, BNP candidate Carlos Cortiglia finished last in the mayoral contest, with 28,751 votes or 1.3% of those cast.
This represented a sharp decline on its 2008 result, when its candidate Richard Barnbrook finished fifth and polled 69,710 votes, ahead of UKIP and Respect.
Mr Barnbrook was at one time a member of the London Assembly for the BNP, later sitting as an independent before retiring.
Other party candidates announced so far include:
The BNP has said it will enter the race to be mayor of London, after acknowledging a "scaling down" at the general election.