Peter Kelly, of Purley, was prosecuted after his pet attacked a herd of Jacob sheep in Riddlesdown Common.
The dog left one sheep so badly injured it was put down following the attack in May last year.
Park rangers found the Staffie shortly after the attack and the City of London Corporation, which owns the land, took Mr Kelly to court.
He pleaded guilty to failing to keep his dog under control at Croydon Magistrates' Court last week was was fined £600.
Allan Cameron, head ranger at Riddlesdown Common, said: "We welcome responsible dog walkers to Riddlesdown but it is vitally important that they keep their dogs under effective control – especially where livestock are present.
Magistrates also ordered Mr Kelly to pay £95 compensation and a £100 contribution to prosecution costs.
The corporation uses sheep and cattle to graze on the common rather than mowing the grass with machinery, which would prevent wildlife such as flowers and insects from flourishing.
The Jacob breed, recognizable by their horns and spotted bodies, is named after the Biblical character, a sheep breeder.