Caroline Hadfield claims her six-year-old son Josh developed the condition just three weeks after being given the jab.
She has set up a website to see if other children have developed the symptoms after taking the drug called Pandemrix.
But the makers claim there is no evidence of any connection and point out that only seven children have developed the syndrome from six million doses of the vaccine in the UK.
The vaccine is manufactured by GlaxoSmithKline, whose UK medical director Dr Pim Kon, said: “There is currently no evidence at all to suggest there is a causal link between Pandemrix and narcolepsy.
Read More: Parents claim link between flu vaccine and narcolepsy