Trump made the announcement during his annual State of the Union address to Congress on Tuesday.
It was not immediately clear in which Vietnamese city the meeting would take place. Possible locations are the capital, Hanoi, and the seaside city of Danang.
“As part of a bold new diplomacy, we continue our historic push for peace on the Korean Peninsula,” Trump told Congress.
“Much work remains to be done but my relationship with Kim Jong Un is a good one.”
Kim and Trump met for the first time in June last year in Singapore.
That summit produced a vaguely worded pledge on denuclearisation but progress has since stalled amid disagreements over the interpretation of their agreement.
On Wednesday, Stephen Biegun, Washington’s envoy for North Korea, was scheduled to hold talks in Pyongyang to map out what he called “a set of concrete deliverables” for the second meeting.
In his speech on Tuesday, Trump also gave himself credit for averting a major war on the Korean peninsula.
“If I had not been elected president of the United States, we would right now, in my opinion, be in a major war with North Korea,” he said.
Trump raised fears of war in 2017 when he threatened to rain “fire and fury like the world has never seen” on North Korea because of the threat its nuclear weapons and missiles posed to the United States.
But following the Singapore talks, Trump has been eager to hold a second summit in spite of a lack of concrete progress in persuading North Korea to give up its nuclear weapons programme.
The Singapore summit yielded a vague commitment from Kim to work toward the denuclearisation of the Korean peninsula, where US troops have been stationed since the 1950-53 Korean War.
In the US view, North Korea has yet to take concrete steps to give up its nuclear weapons. It has complained that the United States has done little to reciprocate its freezing of nuclear and missile testing and dismantling of some nuclear facilities.
North Korea has repeatedly urged a lifting of punishing US-led sanctions, a formal end to the war, and security guarantees.