John and Margaret Lawson and their children Theresa and Mark have condemned the "monstros-ity" built in St Peter's Cemetery in Glasgow's London Road.
Kevin Lawson was just 19 when he was stabbed to death in Tollcross on March 8, 2003.
George Monaghan, 27, from Partick, was jailed in February 2004 for 11 years for culpable homicide.
Kevin's final resting place has become a place of solace for his family who regularly visit the grave.
But on Saturday, mum Margaret, 57, noticed the wind turbine in the cemetery when she was walking along London Road.
Mum-of-two Theresa, 36, went to visit her brother's grave with her 10-year-old son, and was horrified to discover the turbine right next it. She said: "It was terrible. My son said 'mum that's horrible'.
"My mum and dad were totally distraught.
"Mum and dad go over quite a lot for a bit of peace and quiet and a bit of time to be there with my brother and now this monstrosity has been put up right next to him."
The family also own two other plots next to where the turbine has been erected and say they weren't consulted about its construction.
The turbine is in the car park but Kevin's grave is next to it in a plot specially chosen as a quiet place and to make it easier for John, who has difficulty walking, to visit.
John said he was shocked and disgusted when he saw the 40ft wind turbine which makes a "buzzing noise".
He said the grave site "is precious to us".
He added: "It is the place where you can go, and we can sit there and gather our thoughts and have a wee cry.
"But we probably won't be able to hear ourselves cry now.
"They have taken any wee bit of peace – they have just taken it away."
John said the wind turbine is a "terrible thing."
He said: "With the amount of ground they have out the back right down to the Clydeside, nobody should be able to see that thing.
"It should have been put up there, but instead of that it was put up in the car park, which I think is ridiculous.
"We bought this plot because it was out of the way of everybody, next to the car park.
"It was fine and they kept the place lovely, and then all of a sudden that thing appeared.
"I bought two plots there for the rest of my family so they have somewhere to rest, but there is no rest now."
The family are calling for the turbine to be removed.
Theresa said: "We really want something done about it. We want it removed.
"I understand you need these things but I don't think the graveyard is the place for it.
"There is quite a bit of ground at the back of the graveyard where it maybe could have been put back a bit rather than being put in a car park so close to my brother's grave."
John added: "I would like it moved. They have got plenty of ground to move it to. But I wouldn't like it moved to upset somebody else."
A spokesman for the Archdiocese of Glasgow, said: "We applied for all the necessary permissions from Glasgow City Council and complied with all the requirements for installations of this type.
"We were careful to ensure that there would be no noise from the turbine to disturb visitors and relatives and ensured that its placing was as discreet as possible, located at the rear of the visitor car park, on the boundary of the cemetery overlooking the Clyde.
"The installation is a major investment in the development and mainten-ance of the cemetery.
"All financial benefits will be used solely for the cemetery's upkeep."
Planning permission for the wind turbine was granted on September 28, last year.
A spokeswoman from the city council said that all conditions of planning permission were met and no objections were made, therefore there was no reason not to grant permission.