Preheat the oven to 175°C (347°F).
Mash the bananas with a fork.
In a bowl, cream together sugar and butter.
Add the eggs and mix well.
Add the mashed bananas and vanilla extract.
Sift the flour, baking soda, and salt in a separate bowl.
Gently fold the dry ingredients into the batter.
Add walnuts and mix.
Pour the batter into a baking pan.
Bake in the preheated oven for 50 minutes.