An exhaust purification system is provided with an NOx storage reduction catalyst arranged in an exhaust passage and an SOx trap material arranged upstream of the NOx storage reduction catalyst and removes SOx contained in exhaust gas. A main flow path has a secondary flow path connected to it. In the secondary flow path, a removal device is arranged for removing the sulfur constituent contained in fuel. The secondary flow path includes an opening and closing device. When the SOx removal rate of the SOx trap material becomes a predetermined removal rate judgment value or less or the concentration of the SOx which flows into the SOx trap material becomes a predetermined concentration judgment value or more, at least part of the fuel flowing through a main flow path is made to flow into the secondary flow path and run through the removal device.