Whisk brown sugar, soy sauce, garlic, sesame oil and ground ginger together in a bowl; pour into a resealable plastic food storage bag. Add cubes of steak, coat with the marinade and squeeze out excess air; seal the bag. Marinate in the fridge for 2 hours, flipping the bag several times as the beef marinates.
Preheat barbecue for high heat and lightly oil the grate.
Remove beef from the marinade. Discard the remaining marinade.
Thread steak, pineapple, green pepper and red pepper onto skewers.
Cook the skewers on the preheated grill, turning frequently until nicely browned on all sides, about 10 to 15 minutes or until the steak is cooked to your liking.