Position rack in the middle of the oven and then preheat oven to 350 degree F.
Grease and flour a 9X5-inch loaf pan and then set aside.
In a large mixing bowl, cream butter and sugar until light and fluffy.
Add mashed bananas, eggs and vanilla. Beat well until well mixed.
In a separate bowl, sift together flour, baking soda and salt.
Add flour mixture to the creamed mixture. Mix until combined, making sure not to overmix.
Pour into prepared loaf pan and bake for 55 minutes or until toothpick inserted in the middle comes out clean. Cool bread in pan for 10 minutes. Remove bread from pan and transfer to a wire rack. Cool completely before slicing.