Exhaust purification system of internal combustion engine

An exhaust purification system of an internal combustion engine in which a hydrocarbon feed valve for feeding hydrocarbons is arranged inside of an engine exhaust passage, an exhaust purification catalyst for reacting NOx contained in exhaust gas and reformed hydrocarbons is arranged inside of the engine exhaust passage downstream of the hydrocarbon feed valve, the exhaust purification catalyst is comprised of an upstream-side catalyst and a downstream-side catalyst arranged in series at an interval from each other, the upstream-side catalyst has a smaller cross-sectional area than the downstream-side catalyst and has a function of at least reforming hydrocarbons which are fed from the hydrocarbon feed valve, a precious metal catalyst is carried on an exhaust flow surface of at least one catalyst of the upstream-side catalyst and the downstream-side catalyst and a basic exhaust gas flow surface part is formed around the precious metal catalyst, the exhaust purification catalyst has a property of reducing the NOx which is contained in exhaust gas if a concentration of hydrocarbons which flow to the upstream-side catalyst is made to vibrate by within a predetermined range of amplitude and within a predetermined range of period and has a property of being increased in storage amount of NOx which is contained in exhaust gas if the vibration period of the hydrocarbon concentration is made longer than the predetermined range, and, at the time of engine operation, the concentration of hydrocarbons which flow to the upstream-side catalyst is made to vibrate by within said predetermined range of amplitude and within said predetermined range of period to thereby reduce NOx which is contained in exhaust gas in the exhaust purification catalyst.