Crimes such as vandalism to municipal flower beds and the bandstand have cost hundreds of pounds to repair, and reported incidents of under-age drinking have also increased.
It had been Alton Town Council's intention to close the park during the hours of darkness. But the town's new police chief, Inspector Steve Mote, said this would be tantamount to "giving into them".
Inspector Mote said: "I would much rather see greater police patrols in the public gardens so that the problem can be tackled rather than relocated.
"The extra patrols are designed to not only nip the problem in the bud, but to also ensure those who are not guilty of causing trouble do not have to pay the price as well.
"We will arrest anyone found causing any sort of damage in the park, and in any cases of under-age drinking, the drink will be confiscated and all parents will be informed. It also raises questions about where these youngsters are getting the drink," said Inspector Mote.
He added: "Parents also have a big part to play in preserving our park. We know that not all kids who visit the gardens of an evening cause trouble, indeed, it is only a handful that do. But if parents know that their children are going to the Public Gardens in the evenings, then we appeal to them to keep a close eye on their children's activities."
Inspector Mote has asked the town council for six months in which to improve the situation before any final decisions are made on evening closure.