Stir together the teriyaki sauce, soy sauce, brown sugar, and Worcestershire sauce in a large bowl. Place pineapple and garlic in food processor or blender and blend until smooth. Add pineapple and garlic mixture to sauce.
Pour mixture into a 1 gallon resealable plastic bag. Add the beef, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator over night or for 6 to 8 hours.
Place meat on smoker for 6 to 8 hours. The meat should remain a little chewy but not crisp. Store jerky in the refrigerator.