The U.S. Presidential hopeful is quite complimentary towards the North Korean dictator
The outspoken Republican candidate said it was "incredible" how the leader of the totalitarian communist regime had consolidated his grip on power.
It is the latest controversial comment by the property billionaire who has praised the Russian President Vladimir Putin, referred to some Mexicans as "rapists and criminals", mocked a disabled reporter, and called for a ban on Muslims entering the US.
Mr Kim has carried out a series of purges since taking over in 2011 following the death of his father.
Victims have included his own uncle, Jang Song Thaek, who was executed for alleged treason in 2013.
Last year, he is said to have had ordered his then-defence chief, Hyon Yong Chol, to be killed with an anti-aircraft gun for falling asleep in a meeting.
Speaking at a rally in Iowa, Mr Trump said: "If you look at North Korea, this guy, he’s like a maniac. OK?"
But he added: "You've got to give him credit. How many young guys - he was like 26 or 25 when his father died - take over these tough generals, and all of a sudden - you know, it’s pretty amazing when you think of it. How does he do that?".
He went on: "Even though it is a culture, and it's a cultural thing, he goes in, he takes over, he’s the boss. It's incredible.
"He wiped out the uncle, he wiped out this one, that one. This guy doesn't play games and we can't play games with him. Because he really does have missiles and he really does have nukes".
His remarks come amid heightened tensions between North and South Korea after Pyongyang claimed it had successfully tested a hydrogen bomb.
It led Seoul to resume propaganda loudspeaker broadcasts across the border, which have previously been condemned by the North as an act of psychological warfare.