The family of Indi Gregory is appealing to the European Court of Human Rights (ECHR) to stop the withdrawal of life-sustaining treatment.
An application has been submitted to the court by the family after the Court of Appeal this week ruled that it was in the 8-month-old baby's "best interests" to die.
Indi suffers from a rare mitochondrial disease and doctors caring for her at the Queen's Medical Centre in Nottingham believe that life-saving treatment should end.
Her parents, Dean Gregory and Claire Staniforth, maintain that despite Indi's disability, she is a happy baby who responds to their touch.
They are being supported by the Christian Legal Centre which said that the family are appealing to the European court in Strasbourg, France, on the grounds that the High Court trial was "procedurally unfair as the Trust was allowed to provide expert opinion evidence, without having any formal permission to do so or being instructed as experts, and yet Justice Peel refused to allow Mr Gregory to instruct experts in either mitochondrial disorders, neuroradiology or cardiology to support his case".
The family are now waiting to see if the ECHR will accept their case.
Mr Gregory said: "The whole experience of the court system is completely one-sided. From day one all we ever wanted was for Indi to have a fair trial and to be allowed to have an independent specialist, not affiliated with the NHS, to provide expert evidence. What you would think is a fair and basic wish and right, however, has been denied to us and we have not been given that opportunity.
"This is the life of an 8-month-old baby who is being discriminated against because of her disabilities and is being denied the right to a fair trial.
"Because the hospital doesn't understand Indi's complex condition they have given up on her and would rather let her die than allow us to seek international help and expertise. To us, Indi is everything, and is worth the cost and fighting for to give her a chance to live.
"As parent's we believe it is our duty to do everything we can to protect our child. Claire and I are both heartbroken that the courts and NHS are not doing more to help us. It shouldn't be anybody's right to end somebody's life.
"We now hope and pray that the ECHR takes forward the case."
