Teenage vandals have destroyed eight trees in the sensory garden at Eastwood Park.
Police attended the park in Hasland at about 2am on Monday to speak to the young yobs and move them on.
A Hasland resident, who did not want to be named, said: “Why were these young offenders in the park at that time of the morning?
“Some parents seem to think that when their child reaches a certain age they are not their responsibility – but they are.”
Police have pledged to step up patrols in Eastwood Park and Queen’s Park following complaints about anti-social behaviour.
Officers will work alongside council workers to catch culprits in the act.
Sergeant Dave Harrison, of Derbyshire police, said: “Officers will be stepping up patrols at peak times and speaking to any offenders, taking appropriate action where necessary.
“We hope to diminish any concerns as we want to ensure these open public spaces remain as nice and relaxing places for people to enjoy.”
Meredith Ezard, from Chesterfield Borough Council, said: “We believe that by using a multi-agency approach to tackle these issues we can make a difference for the local residents and visitors.”