Preheat the oven to 350°F and generously grease a 9-1/2 x 5-1/2-inch loaf pan.
Cream the butter and sugar together in a large mixing bowl until well blended.
Add the eggs and beat until light and fluffy.
Add the bananas, sour cream, and vanilla and beat until smooth and creamy.
Sift the flour, baking powder, baking soda, and salt together into a separate bowl.
Gradually add the dry ingredients to the wet, stirring just enough to combine thoroughly.
Transfer the mixture to the prepared loaf pan.
Bake for 55 to 60 minutes or until golden brown and a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a rack to cool completely.
Tips for Making This Recipe
Banana Nut Bread Variation
If you like nuts in your banana bread you can add 1/2 cup of finely chopped walnuts to the butter and sugar mixture at the same time you add the bananas, sour cream, and vanilla (Step 4).