Preheat oven to 350F degrees. Butter and flour 9x5 loaf pan.
Whisk together flour, baking powder, baking soda, and salt in large bowl. In another bowl, mash bananas with fork. Then whisk in sugar, oil, peanut butter, eggs and vanilla. Whisk in dry ingredients mixture, just until combined.
Pour batter into pan, smoothing top. Bake until wooden pick inserted comes out clean (about 65 to 75 minutes). Turn bread out onto rack and cool completely.