Mix together ground beef, ginger, garlic powder, and pepper until well combined. Form into 1 1/2-inch meatballs.
Saute meatballs in a large frying pan over medium-high heat until browned, about 10 minutes. Remove meatballs to a plate, reserving the pan drippings.
While the meatballs are cooking, pour juice from the canned pineapple into a liquid measuring cup and add enough water to make 1 cup. Mix brown sugar and cornstarch in a small bowl.
Add pineapple juice and brown sugar mixtures to the warm pan drippings. Add vinegar and soy sauce and bring to a boil. Cook until sauce thickens, 2 to 3 minutes. Add meatballs, pineapple chunks, and green pepper. Simmer until meatballs are no longer pink inside, about 10 minutes.