Exhaust purification system of an internal combustion engine

In an exhaust purification system of an internal combustion engine (1) that includes a NOx catalyst (16) for occluding and reducing NOx in exhaust, when removing SOx deposited in the NOx catalyst, a concentration of sulfur in a fuel is detected, and an amount of SOx deposited in the NOx catalyst is estimated taking into consideration the concentration of sulfur in the fuel. Further, an air-fuel ratio of exhaust flowing into the NOx catalyst (16) is changed to a richer side air-fuel ratio depending on a decrease in the estimated SOx amount, thereby adjusting an HC concentration of exhaust flowing out from the NOx catalyst (16) to a level equal to or less than a permissible HC concentration.