In an internal combustion engine, inside an engine exhaust passage, a hydrocarbon feed valve (15) and an exhaust purification catalyst (13) are arranged. The carrier (50) of the exhaust purification catalyst (13) is formed from a crystallized composite oxide of aluminum and an alkali earth metal. On this carrier (50), precious metal catalysts (51, 52) are carried. The concentration of hydrocarbons which flow into the exhaust purification catalyst (13) is made to vibrate by within a predetermined range of amplitude of a 200 ppm or more and within a predetermined range of period of 5 second or less, whereby the NOx which is contained in exhaust gas is reduced at the exhaust purification catalyst (13).