After becoming a citizen, can I still use my Korean passport as well as my U.S. passport?

If your citizenship was acquired after birth — for example, obtaining a green card first and later naturalizing — rather than being a citizen from birth, then the moment you acquire U.S. citizenship, your Korean citizenship is automatically extinguished under Korean nationality law. This also applies the same way to any children’s passport situation. In other words, the moment you become a U.S. citizen, you no longer hold Korean citizenship, so a Korean passport becomes meaningless.