I can't think of any situations where I would use "grow-up" with a hyphen. Otherwise "grow up" (sans hyphen) is usually used in English as an imperative. "Hey, man! Grow up! Quit acting like a child!" The primary difference between "grown up" and "grown-up" would be that "grown-up" would exclusively be used as a compound adjective to modify a noun. "My daughter is a child. I am a grown-up. Without the hyphen it functions as a verb. That being said, I don't think the average English speaker wouldn't necessarily notice, or care, if you used the un-hyphenated "grown up" instead of "grown-up."