A lot of times, the main reason for a persistent appetite has to do with food quality rather than food quantity. Some examples of food choices that will leave you hungry:
Eating junks carbs
Not eating protein or enough protein
Not eating complex carbs with a good dose of fiber
Not eating enough fat

Concentrate on food quality and calorie distribution throughout the day. Try things like:
Eat more calories during breakfast and lunch
Have a good dose of protein with each meal
Never eat carbs without protein
Have some good fat at every meal
Eat plenty of fiber
Get some of that fiber from raw veggies (lots of chewing!)
Drink plenty of water
Have some protein and healthy fat, plus fiber with every meal, to provide satiety as well as slow the emptying time of the stomach.
Try an apple and some nuts, or cheese and whole grain crackers.
Start keeping a food diary of what you are eating. Note how much you eat and how you are feeling when you eat is it true hunger, or is it related to boredom, depression, stress, anxiety, excitement, or fun? It may bring awareness to your eating habits.