The WMUR Granite State poll found that Brown has gained 10 points on Shaheen in a month. In July, she had a 12-point lead, but the latest survey found 46 percent of respondents selecting Shaheen and 44 percent Brown.
But 60 percent of respondents said their choice was not final.
Brown, a former Massachusetts legislator, won a special election in 2010 to replace Sen. Ted Kennedy, D-Mass., becoming the first Republican in decades to be elected to the Senate from the state. In 2012, he was defeated by Democrat Elizabeth Warren.
In late 2013, Brown sold his house in Massachusetts and established himself as a New Hampshire resident.
Brown faces two challengers in the Republican primary. But he has already received the endorsement of former Massachusetts Gov. Mitt Romney, who has a summer home in New Hampshire.
"I feel very good because when I'm going out and about into people's businesses, holding town halls -- town halls are an important thing -- and conveying my thoughts about being an independent voice for New Hampshire, it's resonating," Brown said.
The University of New Hampshire Survey Center polled 827 adults by telephone between Aug. 7 and Aug. 14. The margin of error is 3.4 percentage points.