A high pressure discharge lamp lighting device for reducing flickering of a high-pressure discharge lamp (La) comprising: power feeding means adapted to feeding a predetermined amount of power to a high-pressure discharge lamp (La); means adapted to alternately invert a polarity of a lamp current fed to the high-pressure discharge lamp (La); and control means capable of changing a frequency alternately inverting the polarity and a duty ratio as a ratio of a period of a positive polarity to a period of a negative polarity, wherein: upon start of lighting of the high-pressure discharge lamp (La), after the high-pressure discharge lamp (La) reaches a stable state or reaches a predetermined lamp voltage, the high-pressure discharge lamp (La) is lighted in one or more lighting modes, characterized in that the high-pressure discharge lamp (La) is lighted in at least three lighting modes (mode 1, 2, 3) with a predetermined average power put into the high-pressure discharge lamp (La), a time duration of a positive polarity is equal to a time duration of a negative polarity in a first mode (mode 1), a time duration of a positive polarity is longer than a time duration of a negative polarity in a second mode (mode 2), and a time duration of a positive polarity is shorter than a time duration of a negative polarity in a third mode (mode 3), a second lighting frequency in the second mode (mode 2) and a third lighting frequency in the third mode (mode 3) is equal to or less than a first lighting frequency in the first mode (mode 1), and a time period of the first mode (mode 1) contains at least one cycle of the lamp current with the first frequency, a time period of the second mode (mode 2) contains at least one cycle of the lamp current with the second frequency and a time period of the third mode (mode 3) contains at least one cycle of the lamp current with the frequency, at least one first mode (mode 1), at least one second mode (mode 2) and at least one third mode (mode 3) are collectively defining one set and the one set is repeated. power feeding means adapted to feeding a predetermined amount of power to a high-pressure discharge lamp (La); means adapted to alternately invert a polarity of a lamp current fed to the high-pressure discharge lamp (La); and control means capable of changing a frequency alternately inverting the polarity and a duty ratio as a ratio of a period of a positive polarity to a period of a negative polarity, wherein: upon start of lighting of the high-pressure discharge lamp (La), after the high-pressure discharge lamp (La) reaches a stable state or reaches a predetermined lamp voltage, the high-pressure discharge lamp (La) is lighted in one or more lighting modes, characterized in that the high-pressure discharge lamp (La) is lighted in at least three lighting modes (mode 1, 2, 3) with a predetermined average power put into the high-pressure discharge lamp (La), a time duration of a positive polarity is equal to a time duration of a negative polarity in a first mode (mode 1), a time duration of a positive polarity is longer than a time duration of a negative polarity in a second mode (mode 2), and a time duration of a positive polarity is shorter than a time duration of a negative polarity in a third mode (mode 3), a second lighting frequency in the second mode (mode 2) and a third lighting frequency in the third mode (mode 3) is equal to or less than a first lighting frequency in the first mode (mode 1), and a time period of the first mode (mode 1) contains at least one cycle of the lamp current with the first frequency, a time period of the second mode (mode 2) contains at least one cycle of the lamp current with the second frequency and a time period of the third mode (mode 3) contains at least one cycle of the lamp current with the frequency, at least one first mode (mode 1), at least one second mode (mode 2) and at least one third mode (mode 3) are collectively defining one set and the one set is repeated. upon start of lighting of the high-pressure discharge lamp (La), after the high-pressure discharge lamp (La) reaches a stable state or reaches a predetermined lamp voltage, the high-pressure discharge lamp (La) is lighted in one or more lighting modes, characterized in that the high-pressure discharge lamp (La) is lighted in at least three lighting modes (mode 1, 2, 3) with a predetermined average power put into the high-pressure discharge lamp (La), a time duration of a positive polarity is equal to a time duration of a negative polarity in a first mode (mode 1), a time duration of a positive polarity is longer than a time duration of a negative polarity in a second mode (mode 2), and a time duration of a positive polarity is shorter than a time duration of a negative polarity in a third mode (mode 3), a second lighting frequency in the second mode (mode 2) and a third lighting frequency in the third mode (mode 3) is equal to or less than a first lighting frequency in the first mode (mode 1), and a time period of the first mode (mode 1) contains at least one cycle of the lamp current with the first frequency, a time period of the second mode (mode 2) contains at least one cycle of the lamp current with the second frequency and a time period of the third mode (mode 3) contains at least one cycle of the lamp current with the frequency, at least one first mode (mode 1), at least one second mode (mode 2) and at least one third mode (mode 3) are collectively defining one set and the one set is repeated.