Apparatus for and method of purifying exhaust gas and method of injecting fuel for diesel engine

In an exhaust gas purifying apparatus disposed in an exhaust passage of a diesel engine, an NOx trap catalyst is filled. The NOx trap catalyst uses an NOx absorber which absorbs NOx in an atmosphere with an excess oxygen while releasing the absorbed NOx when the concentration of oxygen is lowered. In the engine, a main injection is executed near a top dead center of a compression stroke. Meanwhile, a post injection is executed in such a manner that the fuel injected by the post injection is burned near such timing that a diffusion combustion of the fuel injected by the main injection ends in an expansion stroke after the main injection. By executing the post injection, the concentration of O2 in the exhaust gas can be lowered and the concentration of HC can be suitably elevated while lowering production of soot.