Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan or line it with parchment paper.
In a large mixing bowl, combine the mashed bananas, granulated sugar, and melted butter. Mix well.
Add the eggs one at a time, beating well after each addition.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, stirring until just combined.
Stir in the vanilla extract.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven 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.