Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x5 inch loaf pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Stir in the eggs one at a time, beating well with each addition. Stir in vanilla and banana. In a separate bowl, sift together flour, baking powder, and salt.
Blend the banana mixture into the flour mixture; stir just to combine. Fold in walnuts. Pour batter into prepared pan.
Bake in preheated oven for 1 hour, until a toothpick inserted into center of loaf comes out clean.