Holly, an eight-year-old Staffordshire bull terrier, has both male and female reproductive organs.
It does not cause Holly any physical problems, but Coventry RSPCA said there had been no interest from adopters.
Kennel supervisor Danni Holder said: "Canine hermaphrodites are very rare, so Holly is a very special dog to us."
She added: "This doesn't cause Holly any physical issues or difficulties, but it might put people off from adopting her.
"It absolutely shouldn't though, as Holly is such a lovely and friendly dog."
The pet, who is "very playful and loves walks", came into the charity's care in 2016 when the previous owner could no longer look after it.
"Holly has such a big 'Staffie smile' which is infectious," added Ms Holder. "We have fallen in love with her and we think she would be a wonderful dog to have at home."
RSPCA chief vet James Yeates said: "Hermaphrodites have both ovaries and testicles and this is rare. Some of these animals have a mixture of genes in their cells.
"It is more common for some males to have some female genitalia and undescended testicles, known as hermaphrodites. But it is also possible to get females with some male organs which would be known as pseudo-hermaphrodites."
A rare hermaphrodite dog has been unable to find a home because potential owners are "put off" when learning about its condition.