To provide a small-sized steam generator which can generate steam in a short time and can quickly control the quantity of generated steam.

This steam generator has an insulating liquid storage vessel 12 to store conductive liquid and a pair of electrodes 14 and 14 arranged in opposition apart from each other within the vessel, and generates steam by applying currents between electrodes through conductive liquid so as to heat the conductive liquid. An AC power source 18 is connected to the electrode, and also this is provided with a current application control means 20 to control the current application and a sensor 22 to detect the temperature within a steaming chamber 24, and this controls the current application, according to the temperature within the steaming chamber, and controls the quantity of generated steam.