Bishop Robert Finn, from the diocese of Kansas City-St Joseph in Missouri, admitted waiting six months before telling police about allegations relating to Revd Shawn Ratigan, one of his priests.
Revd Ratigan was jailed for 50 years after pleading guilty to child pornography charges.
Bishop Robert was sentenced to two years' probation in 2012 after he admitted failing to report the suspected abuse.
He's now resigned from his role and the Pope has accepted, the Vatican said.
It's thought he's been allowed to resign under the clause of "grave" reason that makes him unfit for office.
Normally bishops must wait until the age of 75 to retire.
In a statement Bishop Finn said it had been an "honour and joy for me to serve here among so many good people of faith".
Temporary Archbishop Joseph Naumman said he prayed "that the coming weeks and months will be a time of grace and healing for the diocese".