Carson, a retired pediatric neurosurgeon and the only African-American candidate in the campaign, claims 28 per cent support from likely voters in the Republican Iowa caucus, compared to 19 per cent for Trump, according to a Bloomberg/Des Moines Register poll.
Senator Ted Cruz was third with 10 per cent and Senator Marco Rubio was fourth at nine per cent.
Jeb Bush, a former governor of Florida who was the early frontrunner only to slip into the middle of the pack, is tied for fifth at five per cent.
Carson's standing "has improved in every way pollsters traditionally measure," said J. Ann Selzer, president of Selzer & Co which conducted the poll.
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"This might be a wake-up for Donald Trump."
The survey, with a 4.9 per cent margin of error, is the second in two days that has Carson knocking Trump off his perch in Iowa, an intensely contested state because it votes first in the lengthy US primary and caucus process.
Carson leads Trump 28 per cent to 20 per cent in a Quinnipiac University poll released yesterday, with Rubio in third with 13 per cent and Cruz fourth at 10 per cent.
Ex-secretary of state Hillary Clinton remains the clear favorite for the Democratic nomination.
Carson's success has been somewhat of a mystery.
He is a political outsider who has lacked a consistent message on the campaign trail, speaks so bluntly and candidly that he ruffles feathers, and often flies under the media radar.
Like Trump, he has capitalized on the populist anger with Washington that is coursing through wide swathes of the American heartland.
Carson raised $20.8 million in donations from July through September, more than any other Republican.