The treatment was developed by researchers at MSKCC in New York City, which is working with doctors at the Bristol Children's Hospital.
It works with the child's own immune system to help it recognise and destroy the cancer cells
Neuroblastoma is a cancer of the nervous system, which most commonly occurs in the under fives.
It affects two children a week in the UK and more than half of these will suffer potentially fatal relapses.
The trial has been funded by two charities, Neuroblastoma Children's Cancer Alliance UK (NCCA UK) and Joining Against Cancer in Kids (Jack), which has pledged more than Â£250,000 to bring the Memorial Sloan Kettering Cancer Center (MSKCC) treatment to Bristol.
Macmillan consultant Stephen Lowis said the vaccine stimulated an immune response to neuroblastoma cells in patients who have previously been treated, but had since relapsed.
He said the "novel therapies" should be made available as widely as possible.
A Bristol hospital is to trial a vaccine for the childhood cancer neuroblastoma.