The accusations against Bishop Mixa date to the 1970s and 1980s
The bishop of Augsburg in southern Germany has offered to resign following accusations that he hit children, Church officials say.
Bishop Walter Mixa told the Pope in a resignation letter that his diocese needed a "new start".
The bishop at first denied hitting children before saying he may have slapped them, and apologising.
A stream of abuse allegations in Europe and beyond has rocked the Roman Catholic Church in recent months.
On Thursday Pope Benedict XVI accepted the resignation of the bishop of Kildare in Ireland - Bishop James Moriarty - who said he wanted to play a part in creating a "new beginning" following scandals there.
Bishop Mixa was accused of carrying out beatings at a Catholic children's home in the 1970s and 1980s.
He has not been accused of any sexual abuse. Many of the allegations to emerge against Catholic priests in Germany and other countries concern the sexual abuse of children.
The BBC's Oana Lungescu says the credibility of the Catholic Church in Germany has been seriously eroded by recent scandals and it is under pressure to show it can deal with the issue.
"I ask the forgiveness of all those to whom I may have been unfair and to those who I may have caused heartache," Bishop Mixa wrote to Pope Benedict XVI on Wednesday.
He said he was "fully aware" of his own "weaknesses".
In addition to the abuse accusations, a special investigator has also alleged financial irregularities at a children's home under Bishop Mixa's responsibility, amid reports that thousands of dollars had been spent on antique paintings, garden furniture and wine.
After denying the accusations of abuse for weeks, Bishop Mixa first issued an apology earlier this week, saying he was "sorry for causing many people grief", without elaborating.
The head of the German bishops' conference then asked Bishop Mixa to take a leave of absence until the reports of misconduct were cleared up.
It was not immediately clear whether Pope Benedict would accept the offer of resignation.
On Wednesday the Pope promised to "take action" over abuse against children by priests, in his most direct remarks to date on the recent allegations.