Place mushrooms and fish into a shallow dish. Combine oil, lemon juice, lemon grass, brown sugar, salt and pepper in a screw-top jar. Shake until well combined. Pour marinade over mushrooms and fish and toss well to coat. Cover and refrigerate for 20 minutes.
Thread mushrooms and fish alternately onto soaked skewers. Preheat a greased barbecue or char-grill on medium-high heat. Barbecue or char-grill skewers, turning frequently, for 5 minutes or until fish is cooked through.