My first thought is you bought some "not so fresh" salmon. I hate buying fish and seafood and rarely do from the store.
Here's how I grill mine-fillet, skin on, soak in a bag full of your favorite flavor of bottled marinade-lemon pepper, garlic herb, whatever. Get a fish grilling basket for the fillets, throw some wood chips on for smoke and just grill. Really simple, marinade them overnight. Would probably work well for stronger tasting fish.
Another thing that might help is to take the skin off-the layer of fat between the skin and meat may be contributing to the strong taste. I have always left the skin on, but I have only used this recipe on freshly caught wild salmon.