Stir together the sugar and salt, add the shrimp and toss well to coat. Refrigerate for 30 mins - 1 hour. Place the brined shrimp in a colander and rinse very well with cold water.
It's easiest if you skewer the shrimp through the head and tail forming a "c" so they don't fall through the grill. Grill, turning once, until shrimp are pink and cooked through, about 6 mins.