A NOx absorbent (18) is disposed in an exhaust passage (17) of an internal combustion engine (1), and a control circuit (30) is provided for controlling the amount of fuel injection into the engine (1). The control circuit 30 works to operate the engine at a rich air-fuel ratio by increasing the amount of fuel supply to the engine so that NOx absorbed by the NOx absorbent when the engine was last stopped is released in all amounts and is purified by reduction after the start of the engine until the engine is first operated at a lean air-fuel ratio. This prevents the release of unpurified NOx from the NOx absorbent (18) at the start of the engine. The operation at a lean air-fuel ratio is assumed in a state where almost no NOx has been absorbed by the NOx absorbent (18), enabling the absorbing capacity of the NOx absorbent to be utilized to the maximum degree.