Verstappen faced heavy amounts of criticism at the start of the 2018 season for bad decisions, and ill-judged moves, causing concern over the Dutchman's temper issues.
But the 21-year-old fought back to produce a breathtaking second half of the season, despite having a bit of a brawl with Esteban Ocon in Brazil.
“If you think of yourself at that age, with the exposure and pressure, what he is doing is pretty special,” Brawn told F1's official website.
“What we are seeing with Max is a great maturing of his approach, losing none of his speed and aggression but just being a bit more tempered in terms of how he attacks things."
"In the right car and right team, he's world champion material for sure," Brawn said, maybe referring to Red Bull's switch to Honda power for 2019.
"Max will be the known reference in the team in 2019. That is always helpful in a team to have that continuity, if you have a troublesome car or you have some things to sort out, knowing the driver, knowing how to qualify what he says is very helpful. So, I think it's great for the team."