More than 400 people have signed a petition asking Cardiff City Council to put a 20mph zone outside Radyr Primary School.
Plaid Cymru candidate for Radyr & Morganstown, Michael Deem started the petition.
He says the roads around Radyr need to be made safer for schoolchildren.
“There was an incident outside Radyr Primary School before Christmas, where a car almost knocked down a family, after mounting the pavement.
“People feel so strongly they have even taken the trouble to return their petitions by post.”
20mph zones are recommended by RoSPA, the Royal Society for the Protection of Accidents. They say they are very effective at preventing injuries.
RoSPA say Local Authorities are responsible for deciding where the 20mph zones should be introduced and must always listen to local people.
Mr Deem doesn’t think Cardiff City Council are acting quickly enough and says he plans to take the issue to the Welsh Government.
Councillor Ramesh Patel, Cabinet Member for Transport, Cardiff City Council says it is inappropriate for him to comment at this stage.
He says he will be responding to a related question from a member of the public on Thursday in the Council Chambers.
CJS News have approached Radyr Primary School but so far nobody from the school has been available for comment.