An NOx storage-and-reduction type catalyst is used which exhibits a
saturated NOx storage amount of 5 g or more as NO2 with respect
to 1 liter of a catalyst volume at 500 C., and rich spiking is controlled
so that an actual NOx storage amount of the NOx storage-and-reduction
type catalyst becomes 50% or less of the saturated NOx storage amount.
Since the saturated NOx storage amount is large, the NOx storage
amount is large even when it is 50% or less, it is possible to prolong intervals
of the rich spiking. Then, since NOx storage component stores NOx
preferentially into the sites which are likely to store and release NOx,
a reduction efficiency is high. Therefore, while prolonging the intervals of the
rich spiking and sustaining an effect of mileage improvement, it is possible to
improve the reduction efficiency of NOx.