Barbara Muldoon said the change was "long overdue"
A campaign calling for the 1967 Abortion Act to be extended to Northern Ireland has been launched.
An amendment to the Human Fertilisation and Embryology Bill would, if successful, allow women in Northern Ireland to have legal abortions.
Alliance for Choice spokesperson Barbara Muldoon said the current legislation was outdated.
"Northern Ireland is already 41 years behind England, Scotland and Wales," she said.
"(That's) something that really seems inconceivable, that women in Northern Ireland would be denied a right that their sisters elsewhere in the UK have.
"We think, certainly in Alliance for Choice, that change is desperately needed."