Schools willing to employ and promote LGBT teachers may be eligible for extra funding.
The fund, run by the National College for Teaching and Leadership, offers schools funding of up to £30,000, to hire teachers, or train existing staff.
It has, however, been criticised by some as “profoundly misguided”, as critics say it actually increases discrimination.
The £900,000 fund aims to encourage applications from on the basis of “protected characteristics, as set out by the Equality Act 2010.
Those characteristics include age, disability, gender reassignment, marriage and civil partnership, pregnancy and maternity, race, religion or belief, sex and sexual orientation.
For example a school could apply for extra funding in order to plug gaps in diversity such as if there is a lack of gay teachers, or staff with children.
It aims to plug “diversity gaps”, by providing the extra training to those who need it.
However it has been criticised by think tank Civitas, the founder of which said the scheme, backed by the Department for Education, needs to be careful.
Speaking to the Telegraph, he said: “The assumption behind the Leadership Equality and Diversity Fund is that there has been discrimination if there is not proportionate representation of any of the above groups in leadership roles.
“It is highly likely that this would include every school in the land. A law against discrimination is at least understandable if it relates to an ascribed characteristic that the individual can’t change (such as race), but it makes no sense if the protected characteristic is chosen.”
Mr Green said he thinks promotions should be based simply on talent and ability.
He went on: “I would abolish the whole thing, I think it’s profoundly misguided and the money could be better spent on providing more teachers for children from disadvantaged backgrounds.”
The scheme was also criticised by David Nuttall, a Tory MP, who said it was “absolute nonsense”.
He told the Telegraph: “Discrimination, positive or not, is still discrimination by its very nature.
“The problem is that by having an artificial mechanism in place that guarantees one group special treatment over another not only is it patronising to that group, but by definition it means that others who might be better qualified for promotion are discriminated against.”
Labour’s shadow education secretary Lucy Powell also took aim at the fund, saying the money could be better allocated.
A spokesman for the Department for Education said the scheme aims to support “under-represented groups”, such as ethnic minorities, within senior teams in schools in England.
He added: “Ensuring there are excellent leaders in our schools, to raise the standard of teaching and achieve the best outcomes for their pupils, is a key part of our ambition of extending opportunity to all.
“But good school leadership teams should also reflect the diversity of the teaching profession.”
Schools are encouraged to apply for the scheme this year, after a pilot ran in 2014/15.