A new primary school for Warmley has been confirmed as part of a wave of government funding for 22 free schools.
Cabot Learning Federation (CLF) will open Tower Road Academy on its Digitech secondary school grounds in 2021.
The academy trust said the school would meet future need for primary places as new housing is to be built nearby.
But some parents in nearby Cadbury Heath say more funding is needed for existing schools.
The government money – capital funding – is specifically intended for building new schools.
The chief executive of the Cabot Learning Federation, Steve Tyler, said: “This is different funding; this is a capital project and the per pupil funding will follow as the pupils join the schools.
“It’s not diluting the money that’s already in the authority.
“It will face the same funding formula that other schools face, but we still need to provide places for children in the area.”
Parents whose children attend the nearby Cadbury Heath Primary were concerned about ongoing funding struggles.
One mother told BBC Radio Bristol: “It’s not a good idea; the money is not around to fund it afterwards. They are struggling with money now.”
A father said: “A lot of parents can’t get siblings into the same school, so that would be a good thing.”
Parent Lucy Morgan, from Hanham, said: “It will create competition for other primaries and if they don’t get full classes it will affect their per pupil funding.”
The funding problems in South Gloucestershire schools was also featured in a BBC Two documentary, School, where education funding challenges were highlighted.
This led to the council awarding capital funding, but not money for ongoing needs such as staffing and books.