Preheat the oven to 350 degrees F (175 degrees C). Grease an 8x4-inch loaf pan and set aside.

Sift together flour, baking powder, and salt in a large bowl. Set aside.

Mash bananas in another bowl and stir in eggs and sugar.

Stir the flour mixture into the banana mixture just to combine, then fold in walnuts. Pour the batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center of the bread comes out clean, 55 to 65 minutes.

Remove from the oven and cool on a rack for 10 minutes, then remove from the pan and cool completely. Slice and serve.