Peel and section the grapefruit over a bowl, and squeeze membranes to extract juice. Set 3 cups sections aside, and reserve 1/4 cup juice for vinaigrette. Discard membranes.
Combine grapefruit sections, salad greens, chopped fennel, and sliced onion in a large bowl. Drizzle salad with the vinaigrette, and toss gently to coat. Serve immediately.