
Clean and pat dry the shrimp with a kitchen towel, then set them aside.
In a medium bowl, combine the ingredients for the shrimp marinade: olive oil, lemon juice, garlic, Cajun seasoning, brown sugar, paprika, salt, and pepper. Mix well with a fork.
Add the shrimp to the marinade bowl and toss until they are well coated. Cover the bowl and refrigerate for at least 15 minutes or up to 1 hour.
Preheat the grill to medium-high heat. Thread the shrimp onto the skewers, about 4-5 shrimp per skewer.
Grill the shrimp skewers for 2-3 minutes per side, or until the shrimp are pink and cooked through.
Once done, serve the grilled shrimp skewers hot, garnished with chopped fresh parsley or lemon wedges.