UK Prime Minister Boris Johnson will be there, along with French President Emmanuel Macron and Chancellor of Germany Angela Merkel.
Mr Johnson has said he'll be raising three "crucial issues" at the meeting.
These include "how science and new technologies can help the world deal with climate change and the threats to biodiversity".
Antonio Guterres, who is secretary general of the UN, has told those attending that they shouldn't come simply with fancy speeches, but real ideas about what countries around the world can do to tackle the problems facing the planet.
BBC reporter Nada Tawfik told Newsround more about what we can expect from the meeting. (If you can't see the video below, then click here.)
But it's not just those in power around the world who will be attending the event.
Teen activist Greta Thunberg will be speaking at the summit to put pressure on the leaders to take more action.
At the end of August, she sailed across the Atlantic to make sure she could be there.
The UN summit comes after millions of people around the world protested on Friday as part of a global climate change strike.
A huge global protest is taking place at the moment in countries all across the world.
The strike, which is lasting from 20 to 27 September, aims to encourage world leaders to do more to tackle the issue of climate change.
The event's website explains: "In over 150 countries, people are stepping up to support young climate strikers and demand an end to the age of fossil fuels. The climate crisis won't wait, so neither will we."
In the UK, big events have been held in major cities and towns, and lots of children have missed school to attend them.
Newsround went to marches in both Manchester and Brighton on Friday 20 September to speak to young protesters about why they felt it was important to do this.
Further protests are planned for Friday 27 September.
The events last Friday were not the first time that young people have got involved in protests about climate change - and the fact that they take place on Friday is also significant.
In August last year, Greta Thunberg skipped school on a Friday (against her school's wishes) to protest about climate change.
In the months since, she has inspired a movement called #FridaysForFuture, encouraging other young people to do the same to show world leaders that more needs to be done.
In March 2019, Theresa May - who was prime minister at the time - spoke out against young people taking action like this. She said that student protesters miss out on important learning that can help them "develop into the top scientists, engineers and advocates that we need to help tackle this problem".