Philonise Floyd told the UN Human Rights Council the whole world saw how his brother was tortured and killed.
He said this proved that black lives did not matter in the US.
UN Human Rights chief Michelle Bachelet criticised the "gratuitous brutality" of Mr Floyd's death.
She said the protests were the "culmination of many generations of pain".
Ms Bachelet, a former president of Chile, also urged countries to confront the legacy of slavery and colonialism, and to make reparations.
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Mr Floyd died after a white police officer in Minneapolis knelt on his neck for almost nine minutes. The killing spurred global protests led by the Black Lives Matter movement.
In a separate development on Wednesday, US Senate Republicans unveiled a proposal for police reform, which would discourage tactics like the chokehold that killed Mr Floyd but it stopped short of an outright ban.
It follows a more radical measure proposed by House Democrats earlier in the month, which would include a ban.
- Which US police reform plan might become law?
George Floyd's brother called on UN officials to set up an independent commission to investigate the deaths of African Americans in US police custody, as well as violence against peaceful protesters.
He was speaking by video link at a debate convened by African countries at the human rights council's headquarters in Geneva.
"The way you saw my brother tortured and murdered on camera is the way black people are treated by police in America," he said.
"You in the United Nations are your brothers' and sisters' keepers in America, and you have the power to help us get justice for my brother George Floyd.
"I am asking you to help him. I am asking you to help me. I am asking you to help us black people in America."
He also denounced police treatment of people involved in the protests which swept the US in the weeks after his brother's death.
"When people dared to raise their voice and protest for my brother they were tear-gassed, run over with police vehicles," he said.
The BBC's Imogen Foulkes in Geneva says it is unclear whether the demand for an official investigation will get enough support to be approved.
The Trump administration pulled the US out of the council two years ago and does not attend its meetings, but our correspondent says some countries are understood to be reluctant to back an inquiry which so clearly singles out the US.
More on George Floyd's death
- VIEWPOINT: Tipping point for racially divided nation
- WATCH: 'This is why we are protesting'
- TIMELINE: Recent black deaths at hands of police
- BACKGROUND: Five pieces of context to understand the protests
- CRIME AND JUSTICE: How are African Americans treated?
25 May 2020
George Floyd dies after being arrested by police outside a shop in Minneapolis, Minnesota. Footage shows a white officer, Derek Chauvin, kneeling on Mr Floyd’s neck for several minutes while he is pinned to the floor. Mr Floyd is heard repeatedly saying "I can’t breathe". He is pronounced dead later in hospital.
Four officers involved in the arrest of George Floyd are fired. Protests begin as the video of the arrest is shared widely on social media. Hundreds of demonstrators take to the streets of Minneapolis and vandalise police cars and the police station with graffiti.
Protests spread to other cities including Memphis and Los Angeles. In some places, like Portland, Oregon, protesters lie in the road, chanting "I can’t breathe". Demonstrators again gather around the police station in Minneapolis where the officers involved in George Floyd’s arrest were based and set fire to it. The building is evacuated and police retreat.
President Trump blames the violence on a lack of leadership in Minneapolis and threatens to send in the National Guard in a tweet. He follows it up in a second tweet with a warning "when the looting starts, the shooting starts". The second tweet is hidden by Twitter for "glorifying violence".
CNN reporter arrested
A CNN reporter, Omar Jimenez, is arrested while covering the Minneapolis protest. Mr Jimenez was reporting live when police officers handcuffed him. A few minutes later several of his colleagues are also arrested. They are all later released once they are confirmed to be members of the media.
Derek Chauvin charged with murder
Former Minneapolis police officer Derek Chauvin, 44, is charged with murder and manslaughter. The charges carry a combined maximum 35-year sentence.
Sixth night of protests
Violence spreads across the US on the sixth night of protests. A total of at least five people are reported killed in protests from Indianapolis to Chicago. More than 75 cities have seen protests. At least 4,400 people have been arrested. Curfews are imposed across the US to try to stem the unrest.
Trump threatens military response
President Trump threatens to send in the military to quell growing civil unrest. He says if cities and states fail to control the protests and "defend their residents" he will deploy the army and "quickly solve the problem for them". Mr Trump poses in front of a damaged church shortly after police used tear gas to disperse peaceful protesters nearby.
Eighth night of protests
Tens of thousands of protesters again take to the streets. One of the biggest protests is in George Floyd’s hometown of Houston, Texas. Many defy curfews in several cities, but the demonstrations are largely peaceful.
Memorial service for George Floyd
A memorial service for George Floyd is held in Minneapolis. Those gathered in tribute stand in silence for eight minutes, 46 seconds, the amount of time Mr Floyd is alleged to have been on the ground under arrest. Hundreds attended the service, which heard a eulogy from civil rights activist Rev Al Sharpton.
As the US saw another weekend of protests, with tens of thousands marching in Washington DC, anti-racism demonstrations were held around the world.
In Australia, there were major protests in Sydney, Melbourne and Brisbane that focused on the treatment of indigenous Australians. There were also demonstrations in France, Germany, Spain and the UK. In Bristol, protesters tore down the statue of a 17th century slave trader and threw it into the harbour.
Funeral service for George Floyd
A funeral service for George Floyd is held in Houston, Mr Floyd’s home town. Just over two weeks after his death in Minneapolis and worldwide anti-racism protests, about 500 guests invited by the Floyd family are in attendance at the Fountain of Praise Church. Many more gather outside to show their support.