Combine brown sugar, apple cider vinegar, olive oil, Dijon mustard, and pepper in a bowl for the marinade.
Place salmon fillets into a shallow glass dish and pour 1/2 of the marinade over the fish. Reserve remaining marinade. Cover and refrigerate for 1 hour.
Preheat an outdoor grill for medium heat and lightly oil the grate. Discard marinade from the glass dish.
Grill salmon, brushing with reserved marinade several times, until it flakes easily with a fork, 4 to 6 minutes.
