David McNab, whose application for the post of acting principal teacher in pastoral care at St Paul's High was rejected because he did not have the approval of the Roman Catholic Church, branded the move "ridiculous".
The council is basing its appeal on a number of wide-ranging grounds, including the claim that the tribunal had no powers to make a declaration under human rights legislation.
Glasgow also argues that the tribunal erred in law by concluding that the council had failed to establish a genuine occupational requirement for the post, and misunderstood the evidence about the need for Church approval as to Mr McNab's religious belief and character.
The tribunal ignored "compelling evidence as to why approval was a crucial and determining occupational requirement", according to the council. Its view is that the discrimination was "justified, proportionate and in pursuit of a legitimate aim" - delivering education in denominational schools.
The tribunal found that the need for pastoral care teachers to be Roman Catholics was neither a genuine occupational requirement, proportionate nor in pursuit of a legitimate aim.
It therefore concluded that Mr McNab was discriminated against on the grounds of religion or religious belief and awarded him pound;2,000 in compensation.
Roderick MacKenzie, the tribunal chairman, also ruled Mr McNab had been "unlawfully discriminated against by the respondents contrary to Article 14 of the European Convention on Human Rights by interfering with his right to freedom of religion or belief guaranteed under Article 9 of the European Convention on Human Rights on the grounds of his religion".
Mr McNab said: "It is ridiculous that Glasgow City Council is continuing to fight this case, especially as it is council taxpayers' money that will pay for it when the majority of taxpayers are against religious discrimination."
Mr McNab has now moved to a new school in the city, having taught maths at St Paul's High for 15 years.
He says that "Catholic approval is creating a two-tier system and effectively gives some teachers a private and exclusive jobs club to which they can apply. We should not have a two-tier system. We should have equality for all."
Mr McNab has been privately funding the tribunal action with the help of donations from sympathisers. He said: "I would be happy if anyone wanted to offer support. I will continue to fight this case to its final conclusion."
He has set up his own campaign at firstname.lastname@example.org. The appeal will be heard by the employment appeal tribunal at a date to be set.