A discharge lamp driving device includes a discharge lamp driving section configured to supply a driving current to a discharge lamp, a control section configured to control the discharge lamp driving section, and a voltage detecting section configured to detect an inter-electrode voltage. The control section supplies a driving current including a first alternating current when the inter-electrode voltage is equal to or higher than a first voltage, supplies a driving current including a second alternating current having a frequency which is lower than a frequency of the first alternating current when the inter-electrode voltage is lower than the first voltage and equal to or higher than a second voltage lower than the first voltage, and supplies a driving current including a third alternating current having a frequency which is higher than the frequency of the first alternating current when the inter-electrode voltage is lower than the second voltage.