Willie Scobie says he has had complaint after complaint about the length of the grass around some DGHP properties and that some residents are even beginning to spot vermin in the undergrowth.
Cllr Scobie said this week: "If the council had retained that contract, the job would be done by now.
"I'm sure the length of the grass isn't helping any vermin problem there may be, and I'm told by fellow councillors across the region that this is a problem everywhere, not just in Stranraer."
In a letter to the head of DGHP, he said: "I attended the Ochtrelure/Belmont Community council meeting where the issue of grass cutting was raised by one of its members.
"The Community Council member was seriously concerned with the state of the grass and how it had been "cut" and there were chunks of grass untouched.
"Since then, I have had further complaints about the grass in the Belmont to Old Port Avenue area of the town and how disgusted the people are at its length." Cllr Scobie believes that It is evident that the contract with DGHP is not being maintained.
He said: "I can see for myself at the east end of Stranraer in the play park and amenity ground not being cut which is not only unsightly but a failure on the part of DGHP to maintain the contract previously held by Dumfries and Galloway Council."
When the Gazette visited one of the worst affected areas, Galloway Avenue, with Cllr Scobie the council's combined services staff were out cutting the lawn at Ochtrelure playing fields and the councillor felt this showed a clear example of where DGHP is failing.
He said: "This is a direct contrast. The weeds and dandelions are in danger of taking over and blowing into neighbouring gardens.
"It appears that once again, DGHP are incapable of sticking to their contract - they are simply not providing. But what else can we expect? This is a total disaster."
One resident who has complained about the situation said: "It (the grass) really is too long to sit out and enjoy. This lovely weather is wonderful and we should be able to go out and not worry about what's under the weeds. It just looks such a mess and doesn't do the area any favours.
"When you see the council land being cut, it doesn't seem fair."
According to local Labour MP Russell Brown, when this service was transferred from the Council to an external contractor there were concerns that this would lead to a reduced level of service - and now these concerns appear to have been confirmed.
Now the MP believes there will be growing fears that if the Tory-controlled Council succeeds in its plan - which could lead to the privatisation of services like refuse collection and street cleaning - local people will see a subsequent drop in the level of those services too.
The MP said: "There were always concerns when the Council lost the contract for this grass-cutting work that the result would be a poorer service, so perhaps nobody will be particularly surprised that people are noticing problems so quickly.
"But this will raise further doubts about the subsequent level of service local people will receive if the Tory-controlled Council is successful in pushing through its plans which could see Council services privatised."
A DGHP spokesperson said: "We are aware that there are areas of grass that have not been cut due to a lack of clarity on the areas of ground specified within DGHP's grounds maintenance contract and the ground maintained by the Council.
"Following an estate visit along with Councillor Iain Dick last week, DGHP and the Council have already defined the areas of concern and are working with our respective operatives to get the grass cut as quickly as possible.
"We totally appreciate that tenants and residents have raised concerns, but we have now clarified the areas which our contractor needs to maintain with the Council and we fully expect that everyone will soon enjoy well maintained areas, where for the first time the grass will be lifted."