28/08/2014 11:04 BST | Updated 20/05/2015 10:12 BST

Kelsey Grammer Is Almost 60 But He Wants More Kids

HOLLYWOOD, CA - AUGUST 11: Kayte Walsh and Kelsey Grammer arrives at the 'The Expendables 3' - Los Angeles Premiere at TCL Chinese Theatre on August 11, 2014 in Hollywood, California. (Photo by Steve Granitz/WireImage)

Kelsey Grammer may be 59 years old, a father of six and grandfather of one, but he says he 'can't imagine' not trying for more babies.

The Frasier actor's sixth child was born just a month ago, but he and his wife Kayte Walsh, 34, are already feeling broody.

"I can't imagine not trying for more because it's been incredible," Kelsey told PEOPLE. "As soon as [he] came out, Kayte and I were going, 'Yeah, let's do another one.'"

Kayte gave birth to a son called Gabriel at 8.22am on July 22 2014.

Gabriel's full name is Kelsey Gabriel Elias Grammer, but it is a family tradition to go by your middle name - his dad's full name is Allen Kelsey Grammer.

Kelsey and Kayte also have a two-year-old daughter, Faith Evangeline Elisa, and Kelsey has four other children from previous relationships: daughters Spencer, 30, Kandace Greer, 22, Mason Olivia, 12, and son Jude Gordon, nine.

Kelsey's eldest daughter Spencer gave birth to his first grandchild, - a boy called Emmett - in 2011.

Speaking of the newest addition to his family Kelsey said: "Gabriel's fantastic. He is a lovely kid. He's been real easy and agreeable."

"It's just this overwhelming gratification of being close to life like this. It just gives you such hope and joy.

"I've never felt more alive or more serenely happy than in the throes of life with these young people. I really enjoy it."

However, Kelsey admits that there is one aspect of fatherhood which isn't quite so 'serene' - nappy changing:

"I do more of Faith's now, and [Kayte] has been pretty hands-on with Gabriel stuff. That'll even out in time," he says.

"The bigger jobs are the ones I'm usually asked to do - the phrase now is, 'Daddy, there's a poop.' So, that's the one I'm in charge of."