Disclosed herein are a steam generator capable of preventing water inflow into a cooking compartment and easily discharging water therefrom and a cooking apparatus having the steam generator. The steam generator includes a first part to store water therein, a second part extending from the first part and having a smaller width than the first part, a heater disposed in the first part to heat water in the first part, and a temperature sensor mounted to an outer surface of the first part to detect a temperature of the heater. Whether the steam generator lacks water is determined by detecting a temperature of the heater using the temperature sensor.