Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a mixing bowl, cream together the peanut butter, butter, and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add to the creamed mixture alternately with the milk, beginning and ending with the flour mixture.
Pour the batter into the prepared baking pan. Bake for 30 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then remove to a wire rack to cool completely.