Mr Trump's defence team argued that he cannot face trial after leaving the White House.
But a 56-44 majority voted in favour of continuing, with a handful of Republicans backing the measure.
Mr Trump is accused of "inciting insurrection" when Congress was stormed last month.
Democrats prosecuting the case opened Tuesday's proceedings by showing a video montage of Mr Trump's 6 January speech and the deadly rioting by some of his supporters.
"That's a high crime and misdemeanour," Representative Jamie Raskin of Maryland said of the footage. "If that's not an impeachable offense, then there's no such thing."
Lawyers for the former president argued it was unconstitutional to put a former president through the process at all and accused Democrats of being politically motivated.
The 56-44 split means six Republicans joined Democrats in voting to go ahead with the trial.
Although this shows some bipartisanship, this result implies loyalty toward the former president in his party remains high enough to avoid a conviction.
Starting Wednesday at noon, each side will be given 16 hours to make their arguments in the case.
It is not clear how long the trial will last or if witnesses will be called, but lawmakers on
both sides are said to favour a speedy trial.