The vote, by 262 to 46, delighted animal welfare campaigners but set the parliament on a collision course with the European Trade Commission and the Canadian and American governments, which have been lobbying hard for the law to be scrapped.
Leghold traps work by clamping on to an animal's leg, biting deep into the flesh, and restraining them until the trapper arrives. The animals are frequently left in the traps for several days and they often resort to tearing off their own limbs to escape.
The EU agreed to ban the leghold from 1995 and to ban fur imports from countries still using them. Countries could still export fur to the EU, providing they banned the leghold or adopted "internationally agreed humane trapping standards". The ban on fur imports was subsequently postponed until 1 January 1996.
But intense Canadian and American government pressure forced the EU to reconsider the ban. They claimed it amounted to a trade restriction and threatened to prosecute the EU under international free trade rules.
Last month the European Trade Commission voted to postpone the ban and set itself in direct confrontation with the parliament. The parliament claims that only it has power to delay or scrap the ban because it is an environmental matter. The commission claims that it has the power to scrap the ban, which it regards as a trade matter.
Ken Collins, Chairman of the European Parliament Environment Committee, said it was "entirely disgusted at the behaviour of the commission".
He added: "We are not just interested in trade and the environment but also the effect of trade on the environment. The environment must have equal weight over the way the community operates."
A spokesman for the European Commission said that the dispute was likely to end up in the European Court of Justice. He said: "We look forward to meeting the Parliament in court - there does not seem to be any other way."