A steam generator is provided that includes an external case having an opening that allows an internal space to communicate with an external environment. Additionally, the steam generator may be provided with a supplier that supplies water to the internal space, a heater provided to the opening to generate steam, an outlet pipe having a first side that communicates with the external environment to discharge steam, and a steam discharge controller provided to a second side of the outlet pipe to open/close the outlet pipe according to a presence or absence of a discharge of the steam.