The editorial in DPRK Today said he was a "far-sighted presidential candidate".
Mr Trump recently said he would be willing to meet North Korean leader Kim Jong-un, and has also proposed withdrawing US troops from South Korea.
Analysts said the editorial was not official policy but probably reflected Pyongyang's thinking.
BBC Monitoring says DPRK Today is one of several Korean-language propaganda websites operated by North Korea.
It is not considered authoritative on the views of Pyongyang, and the author of the article is previously unknown.
Another editorial in the official Rodong Sinmun on Wednesday referred to Mr Trump as "vulgar".
The writer, Han Yong-mook - described as a Chinese North Korean scholar - said Mr Trump's policy on US troops would make the North's "Yankee Go Home" vision come true.
North Korea has long wanted US troops to leave the Korean peninsula.
"The day when the slogan becomes real would be the day of Korean Unification," said the editorial, first reported by website NK News.
It suggested Mr Trump's statement that he did not want to get involved in any conflict between North and South Korea was "fortunate from North Koreans' perspective".
The writer also said US voters should reject Democratic candidate Hillary Clinton, calling her "dull".
"The president that US citizens must vote for is not that dull Hillary, but Trump, who spoke of holding direct conversation with North Korea," said Mr Han.
One North Korea observer said the article was "very striking".
"Admittedly it is not exactly Pyongyang speaking, but it is certainly Pyongyang flying a kite, or testing the waters", said Aidan Foster-Carter of Leeds University writing in NK News.
North Korea had earlier this month dismissed Mr Trump's proposal to discuss Pyongyang's nuclear program with Mr Kim as "just a gesture".
"I think his (Trump's) idea of talk is nonsense," So Se-pyong, North Korea's ambassador to the United Nations in Geneva, had told Reuters.
North Korean state media have hailed US Republican presidential nominee Donald Trump as a "wise politician" who could be good for the North.