The England goalkeeper has been outstanding for Everton this season, including a matchwinning performance at Manchester United last month.
Moyes said: “He does a great job for us. He’s a bit off his head at times which everyone knows and is aware of... but he’s a really great stopper, a really great shot-stopper and saves things really, really well. His kicking’s very good as well and he’s getting better.
“I’m hoping these next few years now we’ll see an even more mature Jordan Pickford, more mature in his goalkeeping and more mature in the way he goes about his game, how he helps lead the team and makes the team better.
“But I don’t want his goalkeeping to change because he’s done a really good job.”
Pickford penned a new deal with Everton to 2029 in October.
Moyes also told the club's souvenir magazine: “Jordan wants to show leadership qualities now, because he’s gained that experience from the big boys he’s played with at England.
“You’ve got to remember, when I first had him, he was still young. I think there are bits of his game where he could still be a bit erratic, a bit excitable and things but, ultimately, when it comes down to it, what he does is he keeps the ball out of the net.
“I actually do think he’s turning into more of a leader. One of the things I’ve picked up on here is, whether it be Seamus Coleman or James Tarkowski, they’re all at the players and Jordan does that too.”