In the present exhaust purification system of an internal combustion engine, a particulate filter is arranged downstream of an NOx storage/reduction catalyst device and an S trap device is arranged upstream of the NOx storage/reduction catalyst device. A first fuel supplying device for supplying additional fuel for regeneration of the particulate filter to the exhaust system upstream of the S trap device or into the cylinder is provided. An amount of the additional fuel supplied by the first fuel supplying device is controlled to make the S trap device not release SOx. A second fuel supplying device is provided in the exhaust system between the NOx storage/reduction catalyst device and the particulate filter to make up for a deficiency of the additional fuel supplied by the first fuel supplying device in the regeneration treatment of the particulate filter.