An exhaust gas purification device having a NOx absorbent includes a by-pass passage for by-passing the NOx absorbent, an exhaust gas flow rate control portion for regulating both a flow rate of exhaust gas flowing to the NOx absorbent and the flow rate of the exhaust gas bypassing the NOx absorbent, and a reductant addition portion for adding reductant into an exhaust passage upstream of the NOx absorbent. In this device, when it is necessary to discharge sulfur components from the NOx absorbent, a temperature rise control is executed such that a temperature of the NOx absorbent becomes higher than a predetermined temperature. Next, a rich condition control is executed such that an air-fuel ratio of the exhaust gas flowing to the NOx absorbent becomes one of a substantially stoichiometric condition and a rich condition. The flow rate of the exhaust gas to the NOx absorbent during the temperature rise control is controlled so as to be higher than that during the rich condition control.