Tara Kanji, 65, who left Idi Amin's Uganda in 1972 following the African leader's expulsion of his country's Asian community, said she and her daughter Salimah, 40, were now scared to leave their home.
They said a hate campaign had been launched against them which has seen their car smashed and dead wasps put through their letter box.
Salimah, a social policy student at Edinburgh University, said she had also been assaulted and even stalked by a man with a video camera.
She said: "There have been so many times when we've had abuse shouted at us, horrible things like 'you black b******, I'm going to hang you from the trees'.
"We're just a quiet family, trying to live peacefully in our flat and they are trying to intimidate us.
"We've told the police so many times, but they say they need other witnesses.
"Now things are escalating. Our car got vandalised and we feel scared to speak to the police."
She added: "There are probably other families like us suffering in silence."
Lothian and Borders Police said it was aware of recent incidents and was continuing to investigate.
A police spokeswoman said: "We can confirm we are looking into allegations following a number of complaints."
Local councillor Norman Work said: "It's very disappointing to hear something like this has been taking place.
"Fair-minded citizens should rally round and look out for anything like this happening."
Last month, racists were blamed after an Asian family had their cars smashed with golf clubs and vandalised with battery acid. The two sisters and their brother, whose parents came from Bangladesh, had been subjected to a hate campaign over the last six months. Each of the attacks took place in Whitson Place East in Saughton, where one of the sisters and her brother live in separate flats.
During one incident, a gang of five men wielding golf clubs broke the windows and dented the bodywork of the sisters' vehicles as they sat watching X Factor on television. The siblings, who were too scared to give their names, said they were worried the vandalism against their cars would escalate into violent assaults.
The News has also told recently how a 36-year-old woman from Stenhouse was left fearing for her safety after receiving more than 30 cards and letters racially abusing her two mixed-race children and saying she will end up "6ft under".
The Scotsman
