Some dogs chew on the leash as a way to get attention. When your dog is walking calmly on a loose leash, no one pays attention to him, but when he acts out, the focus shifts directly to him. For many dogs, negative attention is better than no attention at all.
Other dogs are over-aroused, and the easiest way to release tension is to bite on the leash. In the shelter situation, dogs frequently grab and chew on the leash, often when first taken out of the kennel and led with other dogs. The more intense the situation and the more wound up a dog is, the more likely that leash biting will occur.
Then there are dogs who simply prefer to carry something in their mouths; for these dogs, the leash serves as a sort of pacifier.
For particularly mouthy dogs, offer a toy to carry on walks; this is a simple solution for a dog who chews the leash primarily because he enjoys carrying something in his mouth.
Rewarding wanted behavior, ignoring unwanted behavior and using the right walking equipment make all the difference in teaching your pooch calm leash manners.