A number of parents are understood to have removed their children from Thornwood Primary near Partick because of the problem, while others have requested pupils start high school a year early.
An external agency was sent in by the council following complaints about the behaviour of pupils and the matter has been referred to the Scottish Public Services Ombudsman.
Parents claim a group of pupils have been "running riot" at the school and behaving in a violent and aggressive manner towards teachers and pupils.
Two parents told the Evening Times they have asked for their children to start secondary a year early because of the problem.
Families have written a joint letter to Glasgow City Council's director of educa-tion, Maureen McKenna.
A council spokeswoman admitted that there was an issue with bullying at the school but said it had followed the correct procedures to tackle the issue.
It comes weeks after an Evening Times investigation revealed that the council is failing to regularly monitor bullying incidents in its schools - despite vowing to do so five years ago.
In 2009, the authority announced plans to report figures on an annual basis to keep track of any issues but the council's IT system does not support this.
One parent said: "Recently there have been issues with bullying within Thornwood Primary School to the point that several parents have removed their children from the school.
"A group of five children are running riot in the school, they are rude and obnoxious to teachers, to the point one teacher was reduced to tears.
"They are violent and aggressive towards other adults involved with the school.
"They constantly pick and pick at my daughter both mentally and on many occasions physically.
"The school has exhausted every avenue bringing in Childline, police, 'respect me' tutors, circle time and solution orientated approaches.
"Nothing has been effective in deterring these kids misbehaviour. I have now lodged a complaint with the ombudsman.
"I have requested that my daughter gets into secondary school a year early due to the issue over the past two years.
"As parents collectively we sent a letter to the head of education Maureen McKenna which got us nowhere except she referred me to the Ombudsman.
"I feel let down. My daughter is depressed and rapidly losing confidence in her teachers.
"She has missed a lot of school the past year because of this and I am terrified it will get worse.
" I feel people have to know that Glasgow City Council's attitude to bullying isn't what it claims it to be."
Another parent said: "My son too has been bullied by these same children. It is always the same culprits, a handful of children at most.
"However, other children now seem to be mimicking this behaviour as there doesn't seem to be any negative consequences.
"I have written a formal complaint to the school, to which I have not received any response - not even an acknowledgement that they got it.
"I have asked for my son to be taken into the high school a year early. The two other schools in our catchment are over-subscribed, while Thornwood is half empty, so the school is resistant to agreeing to a pupil transfer."
One mum, 42, from Partick said: "I took my daughter out of the school in September. She has learning difficulties and was an easy target. She was terrified to go to school.
"Since I've moved her there have been no problems. The council is just burying its head in the sand."
A spokeswoman for Glasgow City Council said: "There was some form of bullying but the school dealt with it appropriately.
"These allegations were investigated in line with council policy. As a complain-ant was not satisfied with the council's response they referred the matter to the Scotland's Public Services Ombudsman in line with guidance provided by the council.
"It would not therefore be appropriate to further comment on this matter
"We are not aware of any children being removed from the school on the back of the bullying allegations."