An exhaust purifying method and apparatus of an internal combustion engine are provided with an exhaust switch valve for switching a flow of exhaust gas flowing into an exhaust filter. By switching the exhaust switch valve, the exhaust gas is fed from one side and the other side of the filter, thereby stirring the soot (particulates) in the exhaust gas deposited on the filter having a NOx absorbent and an active-oxygen discharging agent supported thereon. Thus, the soot in the exhaust gas is continuously burned. Moreover, the switching of the exhaust switch valve and the rich spike are inhibited from being conducted simultaneously. In the case where the rich spike is conducted in order to discharge and reduce NOx absorbed in the NOx absorbent, the exhaust gas containing a large amount of HC and CO can be prevented from being discharged into the atmosphere without being purified.