Queensland University of Technology administration officer Cindy Prior has been denied leave to appeal her racial discrimination case against three students.

Ms Prior attempted to sue three QUT students under section 18C of the Racial Discrimination Act for $250,000 after they posted comments on Facebook about being asked to leave an Indigenous-only computer room.

Federal Court Justice John Dowsett dismissed Ms Prior's case in November on the grounds it did not have reasonable prospects of successfully bringing a racial hatred case.

On Friday, Justice Dowsett denied her leave to appeal his decision.

She is now facing having to pay costs of up to six figures to students Calum Thwaites, Jackson Powell and Alex Wood.

Section 18C makes it unlawful for anyone to "offend, insult, humiliate or intimidate" another person or group on the grounds of race, colour or ethnicity.

Ms Prior had argued she was unable to continue working face-to-face with white people following a series of Facebook posts made after Mr Wood was asked to leave an Indigenous-only computer lab at QUT in 2013.

"Just got kicked out of the unsigned indigenous computer room. QUT stopping segregation with segregation," he wrote.

The post attracted a number of responses, including one from Mr Powell who wrote: "I wonder where the white supremacist computer lab is."

Mr Thwaites is alleged to have written "ITT N***ers" but that was not proven and he denied being responsible for the post.

AAP