The Secondary Heads Association said the national curriculum tests for 14-year-olds - known as Keystage 3 - offer little useful information to schools and do nothing to tell parents about their children's progress.
John Dunford, SHA General Secretary, said the tests in English, maths and science had simply replaced schools' own internal exams which he said gave teachers much more reliable information.
He claimed the tests distracted children from the real goal of getting good GCSE results and cut into valuable teaching time.
Mr Dunford, a head teacher for 20 years, told heads at their annual conference in Brighton: "I have always regarded Key-stage 3 tests as a complete waste of public money."
Children came to secondary school having already taken national tests at 11, he said. "We educate them, we assess their progress, we educate them some more and then we test them again, keeping our eye on the longer goal of qualifications at 16 or beyond.
"Keystage 3 tests are an irrelevance in this continuous process of learning and assessment. It is time the Government abolished them and spent the money on something more worthwhile."
The tests caused huge controversy when they were introduced by the Conservatives and provoked a national boycott by schools. But while national tests for 11-year-olds form the basis of primary school league tables, school-by- school test results for 14-year-olds are not published nationally.
The tests have been cited as a possible basis for creating so-called value-added measures to determine how well schools teach different types of pupils, but the Government was forced to abandon plans to introduce an "improvement measure" in last autumn's league tables based on a comparison of GCSEs and Keystage 3 tests after many heads condemned the proposal as fundamentally flawed.