Larkhall Laboratories faces three charges alleging that the packaging and a leaflet in a product called Tandem IQ gave a false impression about its effectiveness for increasing children's IQs.
The charges, under the 1968 Trade Descriptions Act, were brought in a test case by Shropshire County Council's trading standards department.
Larkhall Laboratories, which is based in London and is believed to be Britain's biggest supplier of so-called 'IQ-improving' vitamin pills, denies the charges.
Robert Spencer, for the prosecution, told a stipendiary magistrate at Shrewsbury: 'Over the past four-and-a-half years a controversy has raged in the medical and scientific world as to whether vitamin and mineral supplementation can increase the IQ of children, and if it can, in what circumstances. That debate continues.'
The prosecution was not suggesting that a court of law was the proper forum to conduct that debate, he said.
But while there was some consensus between the experts on both sides of the debate, it was the prosecution's case that the effect of the company's product labelling was misleading.
This was because the labelling gave the impression that the vast majority of children would increase their IQs by taking the tablets, regardless of their existing state of nourishment.
The magistrate is being asked to rule on a controversy which started several years ago when a psychologist in Swansea found that pupils in South Wales showed remarkable improvements in their non-verbal reasoning after taking a supplement of vitamins and minerals.
During the case, which is expected to last at least a week, some of the world's leading scientists will face one another.
Mr Spencer told the court that the prosecution conceded there could be a small minority of children whose diet was poor who might increase their IQ. But he added: 'It is quite clear that supplementation cannot increase the IQ of children regardless of their existing nutritional status.'
He said the labelling conveyed a simple message that these were IQ-raising tablets. 'Give these to your child and his or her IQ will be raised,' he said.
The packaging was an invitation to parents to buy the tablets not because they were a dietary supplement but because they had some special properties which would raise a child's IQ.
He said the letters 'IQ' on the packaging, with a picture of a girl and boy reading, were intended to convey Intelligence Quotient.
But the manufacturers were 'hedging their bets' and tried to disguise that on the back by stating that IQ meant 'Ideal Quota'.
Dr Michael Nelson, a lecturer in diet and nutrition at King's College, London, told the court he concluded that between 3 per cent and 10 per cent of children deficient in minerals could benefit from taking supplement tablets, but that did not necessarily mean their intelligence would benefit.
It was very unlikely any improvement in intelligence performance could be obtained in normal British children by them taking vitamin supplements.
The hearing continues.