The latest test was carried out from HMS Vanguard off the east coast of the United States.
The missile's booster rockets failed and it landed in the sea close to the launch site, according to the Sun, which first reported the malfunction.
Trident missiles carry the UK's nuclear warheads - the weapon of last resort.
This is highly embarrassing for both the UK and the US manufacturer of the Trident missile.
British tests of Trident missiles are rare, not least because of the costs. The price tag of each missile is around £17m.
Both the Defence Secretary Grant Shapps and the head of the Navy were on board HMS Vanguard when she fired the unarmed test missile off the East coast of America in January.
It was supposed to have flown several thousand miles before landing harmlessly in the Atlantic between Brazil and West Africa. Instead the missile dropped into the ocean near to where it was launched.
The previous test from a UK submarine in 2016 also ended in failure, when the missile veered off course.
At the time, the Sunday Times reported that the test fire was launched from HMS Vengeance off the coast of Florida.
The paper said the Trident II D5 missile was intended to be fired 5,600 miles (9,012 km) to a sea target off the west coast of Africa but veered towards the US.
The cause of what went wrong remains top secret, the paper reported, but quoted a senior naval source as saying the missile suffered an in-flight malfunction after launching out of the water.
In a statement the Ministry of Defence admitted an anomaly had occurred in the most recent launch. But it also claimed that the HMS Vanguard and its crew had been "proven fully capable" in their operations, and the test had "reaffirmed the effectiveness of the UK's nuclear deterrent".
The statement added that Trident was the "most reliable weapons system in the world", having completed more than 190 successful tests.
Trident is the name of Britain's system of nuclear weapons, and includes submarines, missiles and warheads.
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