The presumptive GOP presidential nominee has 43 percent support among likely U.S. voters, and Clinton has 39 percent, according to the conservative-leaning Rasmussen.
Another 12 percent of respondents say they liked another candidate, and 5 percent are undecided.
In a similar poll last week, Clinton led Trump by 5 points, 44 percent to 39 percent.
This week’s poll shows Trump’s highest level of support against Clinton since last October.
The poll also finds that 75 percent of Republicans and 14 percent of Democrats support for Trump. The presumptive Democratic nominee has the support of 76 percent of Democrats and 10 percent of Republicans.
Trump leads Clinton among men, but Clinton leads among women. The candidates are tied among voters under 40, and Trump leads among older voters.
Clinton holds a large lead among blacks, while Trump leads among whites and other minority voters.
Trump also leads among voters not affiliated with either major party, but 28 percent of those voters say they prefer another candidate or are undecided.
The survey was conducted among 1,000 likely voters from June 28–29 with a 3 percentage point margin of error.
The poll differs from several other recent surveys that have shown Clinton in the lead.
According to the RealClearPolitics average of polls, Clinton has a 5-point lead over Trump, 44.4 to 39.4 percent. A recent Fox News poll showed the Democrat leading Trump by 6 points, and an ABC News/Washington Post poll conducted earlier this month showed Clinton with a 12-point advantage.