Preheat the barbecue for high medium-heat and lightly oil grate.
Whisk together the butter, garlic, curry powder, cumin and salt in a small bowl.
Arrange four large sheets of aluminium foil on a flat surface. Divide the mussels into four even portions and place one portion on each piece of foil. Dot the mussels with the curry mixture. Sprinkle the capsicum and parsley over the top of each portion. Top each with lime slices. Wrap foil tightly around the portions.
Cook the packets on the preheated grill until the mussels have opened, 5 to 10 minutes. Discard any mussels which do not open.
Transfer the mussels to small bowls and garnish each with a lime wedge to serve.