The project, named 'The LGBT Apology', was launched by the Melbourne church following the sudden death of Anglican bishop, John McIntyre on June 6, 2014.
McIntyre was known to be an "alternative voice", campaigning for the rights of homosexuals within the church.
As a symbol of apology, the church will light their steeple purple until the 20th International AIDS Conference which kicks off July 20.
"Galileo...look what the church did to him when he said 'well the earth's not actually at the centre of the universe, it's rotating around the sun'," Bishop John McIntyre said in a video posted on the project page.
"You've got to deal with what is, rather than what you think...should or should not be."
"This is reality, this is where people are sexually," he continued.
In the project, headed by Father Stuart Soley, the church also reaches out to HIV/AIDS sufferers, who he says have been unfairly subjected to stigmatisation.
"I am very conscious of the influence the western churches have on those places which struggle with dealing with HIV-AIDS in huge numbers."
"That influence prevents good preventative strategies and reinforces stigma," Father Soley said.
"Not all Christians in the west believe these things. We want our voice to be heard as well."
The Fitzroy church will mark the start and finish of the 6 day AIDS conference with a Mass, and will also hold silent vigils each night.