There were 69 claims against peacekeepers in 2015, up from 52 in 2014 was 66 in 2013.
Almost a third of the 2015 claims were made in the Central African Republic.
For the first time, the report has also set out all the countries whose soldiers are reportedly involved under a new "name-and-shame" policy.
Overall, 10 peacekeeping missions were subject to allegations in 2015.
The allegations involve military personnel, international police, other staff and volunteers.
According to the UN's latest figures, there are 124,746 personnel serving in 16 peacekeeping missions worldwide.
It has been criticised for failing to act quickly on sexual abuse allegations made against peacekeepers.
Last December an independent panel calling the UN response to allegations in the Central African Republic (CAR) "seriously flawed" and a "gross institutional failure".
It accused senior UN officials of abusing their authority by failing to take action over allegations of abuse by soldiers from France, Equatorial Guinea and Chad.
UN Secretary-General Ban Ki-Moon's report called for an international convention on "crimes committed in peacekeeping operations".
He also urged countries to change their laws so that they apply to sex crimes committed by citizens serving in UN peace operations.
Mr Ban also called for "on-site court martial proceedings" for some crimes and a DNA database of all peacekeepers.
UN peacekeepers operate under the legal jurisdiction of their home countries, making prosecution more difficult.
In February, the UN said it would send home more than 100 peacekeepers from CAR following sexual abuse allegations.
A 10,000-strong UN force took over a peacekeeping mission in the country in September 2014.
After CAR, the second highest number of allegations was at the UN peacekeeping mission in Congo, with 16 cases, followed by Haiti with nine.

Arthur and Joan Frost, from Prestatyn, Denbighshire, lost their daughter Julie Bennet, and her husband Mike in February.
An image of the couple during their last moments was released by their children.
An appeal has raised over Â£275,00 to help them stay in their home in Wirral.
Mr Bennet, 57, a cabinet maker, had been fighting a brain tumour since 2013. He died on 6 February.
Mrs Bennet, 50, a primary school teacher, died five days later.
She had been diagnosed in May 2016 with cancer which began in the liver and kidneys and then spread to other organs.
Mr Frost said: "The way this went was just horrifying. How can it happen? You don't bury your children, it's just not possible."
"It's not the way it's supposed to be," Mrs Frost added.
"There was nobody like Julie. She was there for everybody. She was absolutely fabulous.
"Michael was the nicest man you could ever meet, he really was. He melted your heart, really."
Mr Frost found out he too had cancer just before Christmas but hid the diagnosis from the family for fear of adding to their strain.
"It was quite devastating to know on top of everything else that had happened," he said. "I'm joining the gang, sort of thing.
"We discussed it at length and said 'there's no way we can say anything under the condition they're in at the moment'."
The family's story prompted a flood of donations to an appeal for the Bennets' children, Luke, 21, Hannah, 18, and 13-year-old Oliver.
Luke has now been granted guardianship of Oliver along with a family friend.
Mrs Frost said the response had been "absolutely amazing", adding, "it restores your faith in human nature".
Mr Frost said: "They've got no income, and we thought well, the mortgage has got to be paid, and that basically was what we were looking for.
"And it just went sky high. It went worldwide. People from abroad have been donating. We just can't get our heads around how wide it's gone."

The 17-year-old boy was arrested at an address in Netherton, West Midlands Police said, and remains in custody.
A 65-year-old man was attacked at 18:15 GMT in Owen Street, Kates Hill, Dudley, suffering serious stab wounds to his head, shoulder, chest and back.
Police said he was now in a stable condition in hospital.
Det Insp Greg Evans said: "Thankfully, the man is... recovering well in hospital.
"We are still working to establish a motive for the attack and we are currently questioning a teenage boy, who was arrested yesterday afternoon."
Allegations of sexual exploitation or sexual abuse by United Nations peacekeepers rose by a third last year, according to a UN report.
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The grandparents of three children who were orphaned when their parents died of cancer days apart have said they are "horrified" by what has happened.
[NEXT_CONCEPT]
A teenager has been arrested on suspicion of attempted murder after a man was stabbed on his doorstep in the West Midlands on Tuesday.