Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan.
In a large bowl, combine the mashed bananas, sugar, and melted butter. Mix well.
Add the eggs and vanilla extract to the banana mixture and stir until combined.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just 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 the banana bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.