LinkStaff at Newcastle Dog and Cat Shelter are having problems finding a home for the three-year-old because of his unique appearance caused by a harelip.
The dog, named Duo by shelter staff, was handed in to them by police after apparently being lost or abandoned.
Staff at the shelter said vets had not seen a harelip to such an extent in a dog before.
Head of fundraising Michelle Pyle said: "We've had a few people come and see him and say he's a freak.
"Duo is not a freak, he's just unusual. Not many people can say they've got a dog like that."
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