An internal combustion engine in an engine exhaust passage of which a hydrocarbon feed valve (15) and an exhaust purification catalyst (13) are arranged. If the hydrocarbon feed valve (15) feeds hydrocarbons by a period of within 5 seconds, a reducing intermediate is produced inside the exhaust purification catalyst (13). This reducing intermediate is used for NOX purification processing. At the time of engine operation, the demanded produced amount of the reducing intermediate required for reducing the NOx is calculated. The amount of production of the reducing intermediate is made to become this demanded produced amount by control of the feed amount and feed period of hydrocarbons.