Preheat the oven to 170°C (338°F).
Soften the butter at room temperature.
Add sugar and mix thoroughly.
Add eggs one at a time, mixing after each addition.
Sift in cake flour, baking powder, and matcha powder, then mix.
Add milk to adjust the batter consistency.
Pour the batter into a pound cake mold.
Bake for 35–40 minutes in the preheated oven at 170°C (338°F).
Transfer to a cooling rack and let cool completely.