The park contains the Grade I-listed Pittville Pump Rooms
Police in Cheltenham say they will deal "robustly" with any incidents of anti-social behaviour or criminal damage in the town's Pittville Park.
Officers have been working with Cheltenham Borough Council and other park users to promote safety and stop damage in the Grade II-listed park.
A police spokesman said any underage drinking, graffiti or vandalism should be reported to police.
Pittville Park opened in 1825 and houses the Grade I-listed Pump Rooms.
The police spokesman added: "While the vast majority of people make the most of the park without spoiling anyone else's enjoyment, we have in the past had reports of a small number of people whose irresponsible behaviour causes disruption.
"For the sake of everyone who enjoys the park we are asking people to report incidents so that we can take appropriate action."
The Pittville Park Watch scheme, which comprises of a group of park users who work alongside police, Cheltenham Borough Council officers and ward councillors, will provide additional protection for the park.