The No Pride in Detention float will be accompanied by around 200 campaigners calling for the federal government to allow the gay men known as Nima and Ashkan to settle in Australia.
Prime Minister Malcolm Turnbull is attending the parade and campaigners hope he will hear their message loud and clear.
"We want to use this platform to send a message to our parliamentarians," said float organiser Amy Thomas.
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"(Nima and Ashkan) should be living here in the community, they should be in Australia walking in the Mardi Gras like us. (Nauru) is not safe for gay asylum seekers."
The men met and fell in love at Australia's offshore processing centre on Nauru.
They have been living together in the local community for a year, but a series of attacks have left them traumatised.
"They have been spat at. They have been called names," said the Director or Advocacy and Litigation and the Human Rights Law Centre, Anna Brown.
"They have been repeatedly physically beaten by the people of Nauru."
For the last 8-months the couple have only left their room under escort to buy their weekly groceries.
"We are going mad," said Nima.
"We are losing our mind. We have mental health problems."
The men were persecuted in their homeland and fled to Australia believing it was a place where they could be safely openly gay.
Instead human rights groups allege the Australian government knowingly sent them to a country where gay people face prejudice.
"And in this case knowingly sent Nima - who disclosed his homosexuality to the Australian government - to a place that criminalises homosexuality," said Anna Brown.
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The LGBT rights group All Out is calling for the government to let the men settle in Australia.
"Even where they are now they can face up to 14 years in prison for who they love. And it makes a travesty of the word asylum," said Executive Director Matthew Beard.
The Department of Immigration and Border Protection has denied the couple's claim that staff told them not to hold hands or be affectionate in public.
In a statement it said it is not government policy to settle refugees who arrive by boat in Australia, and that refugees on Nauru may apply to Cambodia for permanent settlement.
