Several very different fish sell under the name "parrot fish" or some derivation thereof. These fish have radically different diets, ranging from coral to fish flakes. In order to keep any of these fish successfully, you need to know what they eat.
The parrot fish or parrot cichlid does not show up frequently in the aquarium trade, despite its bright colors. It's an an omnivore and needs both vegetable and animal foods to thrive. As juveniles, they eat many foods. They will readily take flake and pellet foods, as well as freeze-dried and frozen bloodworms and brine shrimp. Adults need larger foods, like dried krill or Spirulina pellets. While they readily take prepared foods, include vegetable matter and meaty foods in their diet to ensure they get all the nutrition they need.
Parrot Blood Cichlid
The other parrot cichlid, also called the parrot blood cichlid or bicolor parrot cichlid, comes from artificial breeding. It's a hybrid, not found in nature. Some controversy surrounds it in the aquarium hobby as it does not resemble "natural" cichlids and often has trouble with its jaws and swim bladder due to its unusual shape. These fish are omnivores and eat a variety of foods. Some specially made prepared foods have certain proteins and minerals that enhance red pigments and help maintain this variety's red pigmentation.
The parrot doradid is a catfish from South America. It too is an omnivore. However, as a bottom feeder, it takes special considerations to make sure it gets the nutrition it needs. It will readily accept prepared foods, like sinking pellets and sticks designed for aquarium catfish. However, you should supplement its diet with live and frozen foods like bloodworms and brine shrimp. On a special note, you should only feed this fish after lights-out, since it has a nocturnal inclination and feeds best at night.
Marine Parrot Fish
The oceans feature an entire family of more than a hundred species of parrot fish. These parrot fish eat coral and algae. They have sharp beaks, which can crush coral to extract the live, fleshy parts. Their digestive systems reduce the coral to white sand. Believe it or not, this process helps renew and revitalize the reef, clearing areas for new reef-dwelling invertebrates. In captivity, they typically thrive on a combination of specially prepared foods, vegetable matter like nori sheets and some meaty food like mysis shrimp.