Preheat oven to 350 degrees F. Grease a 9x5 loaf pan; set aside.
In a large bowl, use a hand mixer to cream together butter and sugars for 2 to 3 minutes, until well combined and fluffy. Add in the eggs and vanilla and mix well.
Mash bananas together in a separate bowl, then add to the wet ingredients.
Sift the flour, baking powder, baking soda and salt over the wet ingredients, then fold until just combined. Fold in the walnuts.
Pour the batter into the prepared loaf pan. Bake for 55 to 65 minutes or until the bread is set and a knife inserted into the center of the loaf comes out clean.
Allow the bread to cool for at least 20 minutes before serving.