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Two swans have been shot at Capstone Farm Country Park, in Gillingham.
It is believed that the birds were killed by a catapult or ball bearing gun.
The cygnets were killed on separate incidents, which both happened on a weekend.
Last month, one of the animals had an eye injury and died soon after.
Yesterday, another swan was found dead with an injury to the side of its head.
Capstone Farm Country Park reported the matter to police and officers are checking CCTV.
Anyone with information regarding these incidents, or whoever spots people with guns or catapults, is asked to contact Kent Police on 01634 792209, quoting reference 12-0366.