Preheat the oven to 350°F (175°C). Grease and flour a baking pan.

In a mixing bowl, cream together the butter and sugar. Add eggs one at a time, then stir in vanilla.

In another bowl, mash bananas. Mix into the wet ingredients.

Gradually add the dry ingredients to the wet mixture and mix until just combined.

Pour batter into prepared pan and bake for 40 minutes or until a toothpick inserted in the center comes out clean.

Allow to cool before serving.