59-year-old Liam Adams had challenged a guilty verdict over a string of sexual assaults on his daughter Aine.
Adams, formerly of Bernagh Drive in Belfast, is serving a 16-year prison sentence for the offences.
A judge said the court had not been persuaded that the verdict of the jury was unsafe and dismissed the appeal.
That included all grounds of challenge, including claims about pre-trial publicity, lies and inconsistent evidence.
Liam Adams' abuse of his daughter was said to have been committed over a six-year period between 1977 and 1982.
Aine, who waived her right to anonymity, was between four and nine at the time.
Adams consistently denied the allegations throughout a second trial at Belfast Crown Court in 2013.
A jury of nine men and three women found him guilty of 10 offences against his daughter: three charges of rape, four counts of indecent assault and a further three counts of gross indecency.
Dismissed argument
Liam Adams' legal team went before the Court of Appeal to argue that those jurors were not properly directed on how to deal with widespread publicity in the case.
They claimed the level of press, television, radio and online coverage on both sides of the Irish border even before he went on trial turned his case into a national issue.
According to counsel for the appellant, a television documentary sparked widespread media attention.
The court also heard how Gerry Adams had revealed in an interview that his father subjected family members to sexual abuse.
Giving evidence as a prosecution witness at the first trial, the Sinn FÃ©in president claimed his brother confessed to him that he had "molested" his daughter.
Counsel for Liam Adams contended that any jury member would have heard about the case and her client's earlier battle against being extradited from the Republic of Ireland by the time of the second trial in September 2013.
But judges rejected submissions that it put the safety of the conviction into doubt.
Liam Adams appeared by a prison video-link and his wife Bronagh and other relatives gathered in the public gallery.
None of them showed any emotion as all other grounds of challenge were thrown out.
It had been contended that guidance to the jury may have wrongly shifted the burden onto Adams to prove he was innocent.
A further criticism was levelled at the advice given on how to deal with the reliability of the alleged victim's account.
But the judges dismissed every argument, including claims that the defendant's case was not properly put to the jury.
A bid by Sinn FÃ©in leader Gerry Adams' brother to overturn convictions for raping his own daughter has failed at Belfast High Court.