Prepare the grill for direct cooking over medium heat (350° to 450°F).
Remove and discard the tough bottom of each asparagus spear by grasping each end and bending it gently until it snaps at its natural point of tenderness, usually two-thirds of the way down the spear. Using a vegetable peeler, peel off the outer skin from the bottom half of each remaining spear.
Spread the asparagus on a large plate. Drizzle the oil and salt over the top. Turn the spears until they are evenly coated.
Brush the cooking grates clean. Grill the asparagus (perpendicular to the grate) over direct medium heat, with the lid closed as much as possible, until browned in spots but not charred, 6 to 8 minutes, turning occasionally. Serve warm or at room temperature.