Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together the butter and sugar until light and fluffy.

Add the eggs, mashed bananas, and vanilla extract, and mix well.

In another bowl, combine the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Pour the batter into a greased baking pan.

Bake for 30-35 minutes or until a toothpick inserted comes out clean.

Allow to cool before serving.