In a mixing bowl, cream together the 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 and baking powder. Gradually add to the creamed mixture, alternating with the milk, beginning and ending with the flour mixture. Stir in the lemon zest.
Pour the batter into a greased and floured cake 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 turn out onto a wire rack to cool completely.