Preheat oven to 350 degrees F (175 degrees C). Line muffin pan with paper liners.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour and baking powder; stir into the batter alternately with the milk.
Fill paper liners 2/3 full with batter. Bake for 20 to 25 minutes in preheated oven.