The 'Heart Attack' singer was surprised at how normal and approachable the media mogul was when she first met him as a judge on 'The X Factor' USA last year.
She said: "I expected him to be a lot more intimidating. And I mean that in a humbling way, because when people think of Simon Cowell, they think like, 'Oh, the big boss, he's mean to people' or whatever, but he's super down-to-earth ... Actually I don't know about down-to-earth!
"He's pretty fancy, but he's a humble guy. When he walks in a room, it doesn't matter if you're the biggest celebrity or the biggest big-shot in the room, he'll treat you the same as the person who's coming into the room to bring you tea. I thought that was pretty cool."
Despite his lavish lifestyle and expensive habits - including insisting upon having black loo roll in his house and splurging £3000 a week on floral arrangements - Demi, 20, joked his wardrobe could use some updating.
She explained to heat magazine: "The jeans he wears are torn up at the bottom and you can tell that they're not brand new. So there are parts of him that are super-fancy and then other parts that are super down-to-earth."
The pair have build a friendship in spite of their age difference and often exchange text messages, with Demi revealing she even has a special nickname for Simon.
She laughed: "He calls me Gobby, and I guess that means that I talk a lot or something. I call him Grampa or Grandma."