The Equality Commission of Northern Ireland launched a legal case against Ashers Bakery in 2014 after it refused to make a cake for a potential customer because it supported gay marriage.
The customer requested a cake with the Sesame Street characters Bert and Ernie saying the words: "Support Gay Marriage."
In May last year Belfast High Court ruled that Ashers Bakery acted unlawfully under Northern Ireland equality laws, and ordered the business to pay £500 damages to the client it refused.
Ashers Bakery appealed this decision, and now Professor Christopher McCrudden, of Queen's University Belfast, is aiding it with its appeal.
Mr McCrudden was a student, lecturer and fellow at the University of Oxford, and also studied at the elite Yale University in the United States of America.
The Christian Institute, a charity, is supporting Ashers Bakery with its legal fees.
It's director, Simon Calvert, said: "We are delighted to have such a formidable legal expert join an already strong team.
"Professor McCrudden's experience and knowledge of human rights and equality law will be of incalculable assistance.
"We look forward to the hearing and remain confident that the McArthur family have a good case which deserves to win."
At the time of the original decision, the McArthur family which owns Ashers Bakery said: "After much careful and prayerful consideration given to legal advice, we have decided to appeal the judgment.
"We continue to insist that we have done nothing wrong as we have discriminated against no individual but rather acted according to what the Bible teaches regarding marriage.
"As many other people have already noted, Christian beliefs seem to have been trampled over in this judgment and we believe this only has negative effects for our society.
"Our hope and prayer would be that an appeal will allow us and other Christians to live out their faith in Jesus Christ in every part of their lives, including their workplace."
A lawyer has said that if Ashers Bakery loses its case, often referred to as the 'gay cake case', it could have significant legal ramifications for other groups.
For example, a Muslim printers may be forced to print t-shirts with cartoons of the Prophet Muhammad, or an atheist web designer may be forced to produce a website advocating a God who created the world in six literal days.
