A Dog Named Green is a novel about a mythical Welsh dog, a cŵn annwn and the people who loved her. The cŵn annwn (pronounced coon 'anun) were owned by Arawn, the king of the Welsh underworld Annwn, and were endowed with supernatural powers. They hunted down evil-doers and guided the souls of departed deserving persons to paradise.
Bryn Riley, a young lad in the hills of eastern Tennessee, acquired an unusual hound puppy from a local houndsman who wanted to get rid of it because it resulted from his female coon hound being impregnated by an unknown dog. The puppy didn't look like a normal coon hound and was thought by locals to be a Rosemary’s Baby type puppy.
Bryn befriends a girl (Mattie) in high school who is treated as a pariah by local girls because she is different. They start a budding romance and when Bryn takes her on coon hunts she gets to know Green and a mystical connection grows between Mattie and Green. Bryn is tricked by a local beauty (Colleen) into thinking he has made her pregnant and he marries her. Shortly after marrying Colleen and entering medical school, Bryn goes on a last coon hunt of the season with Green. The hunt is interrupted by a call to Bryn summoning him to a local hospital - Colleen has been in a car accident. He gets into a terrible accident himself rushing to the hospital, and ends up badly injured and in a coma. Green is left to fend for herself and passes through a series of short-term caregivers while being associated with mysterious good and evil happenings, depending on how she is treated. A recovered Colleen dies in a suspicious car accident, and Mattie is accused by the local sheriff of murdering her. Mattie flees and, like Green, is helped by a series of persons in her endeavors to avoid arrest, trial, and imprisonment (or worse), all the while worrying about Bryn and Green.
What happens to Bryn, Mattie, and Green addresses the question of whether they are eventually reunited or fated to wander until falling into different and separate futures.