Hi sammili,
Too much of any good thing is no good... Grape is a good source of vitamin C for your son. My son loves it (actually he loves all of his fruits and veggies!) but I only offer it to him about 3 times a week so that he gets to eat other types of fruits too. Have you let him tried raisins? A good source of fibre and iron, a healthy snack.
Be sure to give him other types of fruits and vegetables (at least two servings of each) plus offer him water often to help loosen his poo poo. You can also try to give him diluted prune juice or dried pitted prunes to help pass hard poo poo.