The dog is a three-year-old Saint Bernard/English bulldog mix named Cinnamon, KHOU.com reported.
Animal control officers who picked up the dog said the woman told them she wanted it killed because she could no longer care for her and because the dog kept getting in the garbage.
Cinnamon was taken to a foster family who will take care of her until she is adopted.
"It`s devastating. I work with these dogs every day. They are my life, and when she walked through my door it just broke my heart. She`s a sweet dog and how can somebody shoot a sweet dog?" animal shelter coordinator Nanette Moss was reported as saying.
Cinnamon has been spayed and a vet gave her a clean bill of health and updated her shots.
More about: