Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan with butter or non-stick spray.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Stir in the mashed bananas and vanilla extract until combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, stirring just until combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the banana bread cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.