Olyphant, who plays Raylan Givens in the drama, explained that the programme appeals to a wide range of people.
"I'm very proud of the show," he told the Daily Record. "You don't have to be a dummy to know that in my business it's easy to be embarrassed by a lot of what you do.
"It's a wonderful feeling when you can just say, 'Take a look at it'. I think it's something really special. From my buddies to my mother and her friends, it's nice to be able to say to just about every grown-up you know to watch it, as you are going to like it. It's a lovely experience to be involved in something like that."
The show is based on books by Elmore Leonard, who has said that Olyphant was the perfect person to play Raylan.
"That statement makes your day without doubt," Olyphant said. "It meant a great deal."
He continued: "When I got this job I just thought, 'This is a hell of an opportunity'. This is a character where if you get it right, it's something really special, and they are hard to come by. It's Cowboys and Indians. It's cool, it's sexy, it's funny, it's all the things Elmore does when he's clicking on all cylinders. There's a lot there to like."
Justified premieres tomorrow at 10pm on Five USA in the UK. It continues on Tuesdays at 10pm on FX in the US.