His claims come after last weekend's stabbing of an Iranian refugee in Glasgow and as councils tackle fresh legislation that forces them to eliminate racial discrimination and promote good race relations.
But Mr Anwar says the new legislation will need to be funded by central government. The number of black pupils excluded and suspended from school needs to be monitored and racism by teachers tackled head-on.
He believes no local authorities are up to scratch and calls for far stronger measures.
He told The TESS: "People in schools and in charge of our schools are putting their heads in the sand. But with the murder of Imran Khan in Shawlands a few years ago and recent attacks on asylum seekers in Glasgow, it should be apparent this is a bomb waiting to explode."
Every week, Mr Anwar says, he receives racist complaints against teachers, yet knows of no teacher who has been disciplined. "Like the police, schools investigate themselves and complaints of racism are not taken seriously," he says.
As part of a tougher strategy, he wants black history put in the mainstream curriculum.
However, a Glasgow council spokesman denied the allegations. "There is no 'softly-softly' response to racism and there is no evidence of black pupils being 'failed' by our schools or being more likely to be excluded. In fact, the recent report, 'Starting Again', by Save the Children and the city council, showed that over three-quarters of young asylum seekers saw school as a positive thing in their lives.
"The council treats racism extremely seriously and schools are obliged to report each incident. Education services has had an anti-racist action plan for several years, updated annually," he said.
In Edinburgh, the authority is "proud" of its anti-racist work in schools, highlighted by this week's launch in a city primary of a CD-Rom of good teaching practice on anti-racism,commissioned by the Scottish Executive after the death of Stephen Lawrence, the black Londoner stabbed at a bus stop.
Des McNulty, the new Deputy Social Justice Minister, backed the Learning and Teaching ScotlandEdinburgh University package containing information on the new legislation. The minister said: "The message is simple - there is no place for racism in Scotland."
How racist are our schools? ScotlandPlus, pages 2 and 3