Danner, 72, says even though they belong to a family of celebrities, she never expected Paltrow to be so famous, reported People magazine.
"It was just so darn fast, but she came into the world like that - like this meteor. I think it's worrisome when fame happens to your child so early. Bruce and I, having had careers more modest, never had that kind of scrutiny Gwyneth had, and we never had that kind of pressure.
The mother also expressed her desire to see Paltrow more frequently on screen.
"She's a brilliant actress, and my hope is that as her children get older, she'll be going back to acting more fully.