Adams, the brother of Sinn Fein president Gerry Adams, had denied the charges.
But a jury of nine men and three women found him guilty.
The court had heard how Gerry Adams had gone with his niece Aine to Buncrana in Co Donegal 20 years ago to confront Liam Adams.
He was living in the town at the time.
Aine had claimed her uncle Gerry had threatened Liam with a hammer after hearing of the abuse allegations.
The Sinn Fein leader denied threatening violence during the trial.
Liam Adams, from Bernagh Drive in Belfast, had denied all 10 charges – three of rape, three of gross indecency and four of indecent assault.
The offences took place between March 1977 and March 1983 when his daughter Aine was aged between four and nine years old.
Liam Adams was remanded in custody.