Puppy Nipping and Rough Play

Source: 

The Humane Society of the United States

It's not always easy to convince a new puppy not to bite the hand that feeds him, pets him, or plays with him, for that matter. When puppies play with each other, they use their mouths, so they may also be inclined to bite or "mouth" your hand during play or when being petted. This is rarely aggressive behavior meant to do harm, but it is a difficult habit to break unless you encourage your puppy to try an acceptable alternative behavior. The goal is to redirect your puppy's energy onto acceptable chew toys, and to teach her to be gentle when a hand is in or near her mouth.