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, peanut butter, melted butter, granulated sugar, and brown sugar. Mix well until smooth.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack and let it cool completely before slicing.