They say they are "distraught" at the 40ft "monstrosity" in the car park, next to the grave and two additional plots owned by the family.
John and Margaret Lawson and their children Theresa and Mark regularly visit the final resting place of Kevin Lawson, who was 19 when he died on March 8, 2003.
His sister Theresa, 36, said her mum and dad were "totally distraught" since they first saw the turbine two weeks ago.
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The turbine is in the car park but Kevin's grave is next to it in a plot specially chosen to make it easier for John, who has difficulty walking, to visit.
The family say they were not consulted about the construction of the turbine and believe they should have been.
John said the turbine's "buzzing" noise spoils the peace of the site for the family.
He said: "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."
The family have called for the turbine to be removed.
But planning permission was granted on September 28 last year and a city council spokeswoman said the conditions of planning permission were met and no objections were made.
(NE)
