In order to optimally control power outputted from a high intensity discharge lamp lighting device for a difference among loads connected thereto, such as a difference in gas components contained in arc tubes and a difference in shape of the arc tubes individually in a plurality of discharge lamps 11, plural kinds of output power characteristics W1, W2 and W3 as data tables of lamp voltage-lamp power are provided for a rating lamp voltage range of each of the high intensity discharge lamps 1 and a lamp voltage range lower than the rating lamp voltage range, there is provided minimum lamp voltage detecting means 7 for allowing predetermined power to be outputted in an event of starting the high intensity discharge lamp 11, and detecting a minimum lamp voltage Vmin after the high intensity discharge lamp shifts to an arc discharge, and in response to that the detected minimum lamp voltage Vmin enters any range of a plurality of preset voltage ranges A, B and C, any of the data tables W1, W2 and W3 of the lamp voltage-lamp power, which correspond to the voltage ranges A, B and C, respectively, is selected.