RE: Is eating grass normal or abnormal for your pet ??
first, rest assured that you're not alone in your concern if you dog is eating grass and vomiting.
My dog is also doing this weird thing, so I did some research. I found out that PICA is the technical term for the disorder that characterized by eating things that aren't food. I have read that dogs eating grass, indicates that your dog has some type of nutritional deficiency, though, it is often simply a sign of boredom, especially when practice by puppies or younger dogs.
Other suggested reason why your dog might be eating grass include improving digestion and treating intestinal worms.
Dogs eating grass is quiet common, infact most veterinarians consider it a normal dog behavior. I think that it is their way of treating themselves.