The study has also been criticised as unethical
A study in which fish oil was given to pupils in County Durham has been dismissed as "laughably incompetent".
Durham County Council said children who took the Omega-3 supplements during the school year performed better in exams.
It claimed out of 3,000 students who took part, almost a third showed significant improvements in GCSEs.
Dr Ben Goldacre said it was bad science because there was no separate study of pupils not taking fish oil. The council admits the trial was not definitive.
Dr Goldacre, an award-winning medical writer, said: "I think it is a laughably incompetent analysis of a laughably incompetent piece of research.
"In my view it is unethical to perform incompetent research on children in this way."
However Dr Goldacre added that just because the study was poorly conducted, that did not mean there was no benefit to taking fish oil supplements.
"I do think it's possible that fish oils might be helpful to improve school performance in children."
Dave Ford, from the council's children and young people's services department, carried out the initiative with the help of an educational psychologist.
They matched students who showed improved results to those, of similar abilities and backgrounds, who did not take the tablets.
However, the council explained that there was no controlled study of those children who were not given supplements as part of the study, which took place in the school year ending in summer 2007.
Mr Ford said: "This study has produced some interesting and possibly exciting issues that could be the basis for future scientific trials.
"There seem to be some very clear indications that pupils taking the supplement do significantly better."
Mr Ford added that the council made no claim the results of its GCSE study could be attributed to Omega-3 supplements alone.