He's thought to be the first royal to make such a visit
Prince William was speaking to a group of young people at the London headquarters of the Albert Kennedy Trust (Akt), an LGBT+ charity dedicated to helping young people made homeless because of their sexual orientation.
When asked how he would react to his children potentially being LGBT+, the duke replied: "I think you really don't start thinking about that until you are a parent and I think – obviously, absolutely fine by me."
The talk today is thought to be the first time a member of the royal family has visited a dedicated LGBT+ organisation.
He went on to say: "The one thing I'd be worried about is how they, particularly the roles my children fill, is how that is going to be interpreted and seen.
“It worries me as to how everyone else will react and perceive it and then the pressure is then on them."
He also said that he and the Duchess of Cambridge had been doing a lot of talking about it to make sure they were prepared.
Tim Sigsworth, the Akt's chief executive, said he was “incredibly impressed”, that Prince William's comments would make a "massive difference" and would send "a message that we need to support, and we need to empower LGBT people".
This is not the first time the duke has shown his support for LGBT+ issues. In July 2016 he appeared on the cover of gay magazine Attitude, and used his interview to discuss the impact of homophobia, biphobia and transphobia on young people’s mental health.
Akt was founded in 1989 by Cath Hall, whose 16-year-old foster son died after being the target of homophobic bullying