Residents were shocked to discover that the grass at Crickmere Park had been churned up with tyre tracks earlier this week.
And community councillors are worried that it will be impossible to restore the grass before the winter weather sets it.
At a meeting on Tuesday evening, community councillor Garry Stubbs said: “It has been going on for a long time, they have destroyed the park.
“It is just a free for all, I think we need to get some gates or something to stop the vehicles getting in.”
Fellow member Dougie Macgregor added: “They have been on Graitney field as well, and the children’s park behind Empire Way.
“It just feels like whoever has done it is trying to provoke people, someone could get hurt.”
Annandale East and Eskdale councillor Karen Carruthers said: “It is an absolute disgrace, it is a mess.
“If a dog is off its lead in the park and a quad bike comes in out of nowhere there could be a horrible accident.
“But my concern is if we block them getting onto Crickmere how are we going to protect Graitney? We might just force them to go elsewhere.”
Police are aware of the ongoing issue and an officer told Tuesday’s meeting that measures were being put in place to try and resolve the issue, including additional patrols around parks and playing fields in the town.
She also advised residents to report any incidents as soon as they occur using the 101 number.
A Dumfries and Galloway Council spokeswoman said: “We are aware of the issue and have contacted Police Scotland directly.
“We are currently looking at options of what we could do at Crickmere Park.
“Graitney Field is completely open so it would be extremely costly to install fencing all the way round it to keep one or two irresponsible people out.
“We find this frustrating but would also not want to spoil the area for other users, as has been done here through irresponsible vandalism.”