There are provided NOx trap catalyst to trap and release NOx based on air-fuel ratio, first fuel supply means for supplying gasoline, second fuel supply means for supplying hydrogen, engine operation detecting means for detecting engine operating condition, fuel ratio changing means for changing the ratio of gasoline and hydrogen, NOx release determining means for determining whether it is required for the NOx to be released based on a state of the trapped NOx, NOx releasing means for releasing the NOx trapped by making the air-fuel ratio rich when the NOx releasing requirement is determined, gasoline ratio increasing means for increasing the ratio of gasoline when NOx releasing requirement is determined and the air-fuel-ratio rich control is executed. Accordingly, improper vibrations or noises can be restrained from occurring when the rich air-fuel-ratio control is executed to release the trapped NOx from the NOx trap catalyst.