Preheat oven to 350F degrees. Generously grease a 9-inch loaf pan; set aside.
In a large mixing bowl, beat butter with electric mixer on medium speed for 30 seconds. Gradually beat in sugar until combined. Next beat in banana, eggs and vanilla.
In a medium bowl, combine flour, baking soda and salt. Add dry mixture to the butter mixture alternately with buttermilk. Fold in walnuts. Spoon into prepared loaf pan, spreading evenly.
Bake uncovered for 55 to 60 minutes, or until toothpick inserted in center comes out clean. Cool in pan on wire rack for 10 minutes, then remove from pan and cool completely on wire rack.