Cats that growl while eating were usually the runt of the litter, or have spent some time having to survive in the wild or on the streets. They are used to having to fight for their food. They could also be in pain from dental issues. Once you eliminate the issue of dental pain, you can focus on behavioral therapy. There are a few things you can do to train your cat out of the habit of growling while he eats. Mainly, you will need patience and persistence.
Eliminate any dental issues. Cats will often growl when they are having dental pain while eating. Particularly if this is recent behavior and there have been no changes in the household, such as the addition of a new cat, take your cat to a veterinarian and have her teeth and gums thoroughly examined.
Feed the cat in a separate room if it growls when eating near another cat, or at least feed the cats at a distance from each other. When a cat growls while eating near another cat, it is his way of saying, "This is mine. Stay away." By separating the cat from others, you can relieve some its anxiety about other cats getting his food.
Try petting the cat while she is eating, and see how she reacts. If the cat responds in a positive manner, continue to pet her. This will often calm the cat and reduce her anxiety as she feels feel protected and safe.
Place the cat's food bowl in your lap or on the floor near you. While the cat eats, praise him, speaking in a soft and comforting tone of voice. Pet the cat if he will allow you to do so. Again, this will help to relieve the cat's anxiety, and help it to feel calmer while eating. By doing this on a consistent basis for several days in a row, you may find that the cat no longer growls while eating his food.