The billionaire now has three consecutive wins, after victories in New Hampshire and South Carolina, the BBC wrote.
Senators Marco Rubio and Ted Cruz, who have been attacking each other this week, are vying for second place.
Party officials said they were looking into reports of double voting and not enough ballots at one caucus site.
Some volunteers also wore clothing in support of Mr. Trump, but officials said this was not against the rules.
In his victory speech, Mr. Trump told a roaring crowd of supporters: "We're winning, winning, winning the country, and soon the country is going to start winning, winning, winning."
Nevada, typically a swing state with a substantial Latino population, is crucial to the election process. Hillary Clinton won the state on Saturday in the Democratic race.
