Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the mashed bananas until evenly incorporated.
Pour the batter into the prepared loaf pan and spread evenly.
Bake for 60 minutes or until a toothpick inserted into the center comes out clean.
Remove from oven and let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.