Nominations close on Tuesday 31 July for the inaugural Alan Turing Memorial Award.
The award will recognise individuals or groups who have made a significant contribution to the fight against homophobia in Manchester.
The annual award has been launched by Manchester City Council, in partnership with The Lesbian & Gay Foundation (LGF) to coincide with the centenary of the computer genius' birth.
The award will be a new special category in the LGF's Homo Heroes Awards.
Alan Turing is considered to be the father of the modern computer. In Manchester he created the world's first computer with storable memory. All modern computers - from laptops to iPads - are based on this prototype, which was called the Manchester Computer. His codebreaking work during the Second World War was instrumental in Britain's defeat of the Nazis.
But Turing was also gay. He was prosecuted for having a relationship with a man and was forced to take female hormones to avoid jail. Two years after being convicted, Turing took his own life by taking a bite from an apple he had laced with cyanide.
Councillor Bev Craig, Manchester City Council's lead member for lesbian issues, said: "We felt it was important to mark the centenary of Alan Turing's birth with something special - and what better than the lasting legacy of an annual award for those who have fought against homophobia."
Paul Martin OBE, chief executive of the LGF, added: "The Lesbian & Gay Foundation's Homo Heroes Awards showcase the contributions made by individuals, groups and organisations for, and on behalf of lesbian, gay and bisexual communities. They provide an opportunity to celebrate those that have challenged homophobia and biphobia, as well as those who have achieved significant gains for our communities and provides a very real opportunity for people from within the community to celebrate the achievements of those who have made a real difference."
Councillor Kevin Peel, Manchester City Council's lead member for gay men's issues, said: "This is a unique way to recognise those who have stood up for our city's LGBT people, so I would urge everyone to take a few minutes to nominate someone for this prestigious award."
The Homo Hero Awards are supported by Barclays. Julian Bucknall, Co-Chair Barclays Spectrum (the LGBT Employee Network) said: "At Barclays we believe people are at their best when they can truly be themselves. That is why we are proud to support the LGF in their mission to promote LGBT equality."
Nominations for the Alan Turing Memorial Award - and all the other Homo Heroes categories - can be made on the LGF's website at www.lgf.org.uk/hero.
The winner will be decided by a panel and the award will be presented by Cllr Peel at the Homo Hero Awards ceremony in September. The winner will also be invited to the Town Hall to be received by the Lord Mayor.