Why does your cat vomit after feeding?

This is not normal behaviour. Does your cat only vomit up dry food, or other types of food as well? It sounds like your cat is completely rejecting its food because it cannot digest or swallow it. It is very possible this could be down to the food itself.

Many brands of dry food are packed with corns and grains. This is cheap carbohydrate filler that the food manufacturers use as its a cheaper source of protein than meat is. Cats are strict carnivores, so can only get their nutrients from meat-based protein, not plant-based protein.

Sadly, it is all this carbohydrate filler is probably the reason your cat is vomiting up undigested pieces immediately after eating. Cats cannot digest such a high level carbohydrate at all; the stomach usually ends up working far harder than it should just to try and break the kibble down (a cat's stomach has evolved to break down raw meat quickly - not to store grain). This doesn't help as many cats will just swallow pieces of kibble whole - they will often not crunch the food. The biscuits will often just sit in the stomach for long periods of time and often get converted into fat (this is one of the main causes of obesity) if the cat does manage to digest it. Yes, even vomiting up food the cat has had for years can happen.

It might be advisable to take him to the vets to make sure there is no underlying problem, and to switch him to a grain-free food. There are many wet foods that are high in meat and grain free, but there are also some dry foods out there with no grain such as Orijen. Look at the Ingredients and stay away from labels such as "grain, corn, wheat gluten, grain/corn by product, by product meal" etc.