Police are investigating suspected dog attacks in the past fortnight on three flocks of sheep in the High Hurstwood area near Uckfield.
In the latest incident, a sheep grazing near Burnt Oak Road was badly mauled and had to be humanely destroyed.
Other local farmers have reported injuries to livestock also thought to be consistent with dog bites.
Police said the dog suspected of carrying out the attacks has been described as a large, tan-coloured animal, and when last seen, was wearing a dog coat.
Sergeant Tom Carter said:
“Livestock worrying has a devastating effect on the sheep farming community and is a nationwide problem.
“Responsible dog ownership is the best prevention.
“Please keep your dog safe and do not let it roam away from your property.
“Where appropriate, police will prosecute owners who allow their dogs to attack sheep and under certain circumstances dogs worrying livestock may be shot.”
Anyone with information is asked to report it online here, or phone 101, quoting reference number 779 of 20/12.
Alternatively, contact Crimestoppers anonymously on 0800 555 111.