A report was made to Wealden Police regarding two dogs worrying sheep in Groombridge two days ago.
The dogs killed four sheep before they were shot dead by the farmer.
PC Jen Black of Crowborough Neighbourhood Policing Team said: “These offences are extremely serious and the farmers are fully within their rights to kill any dogs that are worrying livestock.
“It only takes a few seconds for an irresponsible dog owner to cause havoc amongst livestock.
“We would urge all dog owners walking anywhere near livestock grazing, to ensure they have their animals under complete control.
“Do not let your dog off the lead around any animals and keep a safe distance.
“Any dog owners identified will be prosecuted. If found guilty it is very possible that they will be ordered to have their dogs destroyed.
“Also check your garden fences so your dogs cannot escape and worry livestock without your knowledge.”
You can discuss this matter further with your local Neighbourhood Policing team.
Contact details can be found by visiting www.sussex.police.uk