Whisk brown sugar, soy sauce, garlic, sesame oil, and ground ginger together in a bowl; pour into a gallon-sized sealable plastic bag. Add beef, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 2 hours, flipping the bag several times as the meat marinates.
Preheat an outdoor grill for high heat, and lightly oil the grate.
Remove beef from the marinade. Discard the remaining marinade.
Thread beef, pineapple, green bell pepper, and red bell pepper onto skewers.
Cook the skewers on the preheated grill, turning frequently until nicely browned on all sides, and the meat is no longer pink in the center, 10 to 15 minutes.