Police are stepping up patrols in Long Eaton's West Park after a state of damage.
Over the last week, damage has been caused to young trees and out-buildings.
Sergeant Damien Shannon, of Derbyshire Constabulary, said: "The damage seems to be completely without motive.
"We have been speaking to our partners at Erewash Borough Council and increasing our patrols on the park.
"These patrols will be both high-visibility and plain-clothed.
"The particularly upsetting part of this damage is that the offenders are spoiling a facility that is there for all to enjoy and so I would encourage anyone who knows anything about the incidents to make contact with us."
Call officers on 101 or Crimestoppers on 0800 555 111.