An exhaust gas purifying apparatus for an internal combustion engine having a lean NOx catalyst in an exhaust system is provided. The lean NOx catalyst traps NOx in exhaust gases when the exhaust gases are in an oxidizing state, and discharges the trapped NOx when the exhaust gases are in an reducing state. In this apparatus, an estimated trapped NOx amount which is an estimated value of an amount of NOx trapped in the lean NOx catalyst, is calculated using a neural network. Engine operating parameters indicative of an operating condition of the engine are input, and the neural network outputs at least one control parameter which is relevant to the lean NOx catalyst. A reducing process of the NOx trapped in the lean NOx catalyst is performed according to the estimated trapped NOx amount.