Preheat barbecue to medium heat. Rinse the salmon under cold water and pat dry. Make a few shallow cuts through the skin of the fish on both sides. Brush inside and outside of the salmon with olive oil and season with salt and pepper. Place on 3 slightly overlapping sheets of aluminum foil. (Make sure the sheets are large enough to encase the whole salmon).
Trim top of fennel. Half and thinly slice lower portion. Stuff salmon with lemon, fennel slices, garlic, dill or parsley, and a few sprigs of the feathery upper portion of the fennel. Fold foil over the salmon and seal. Place salmon on the barbecue. Close the lid and cook about 15 minutes per side.