An exhaust purification system of an internal combustion engine is provided with a hydrocarbon feed valve arranged in an engine exhaust passage and an exhaust purification catalyst for causing NOX contained in exhaust gas and reformed hydrocarbons to react. The exhaust purification catalyst reduces NOX if a concentration of inflowing hydrocarbons vibrates within a predetermined range of amplitude and within a predetermined range of period and increases the amount of storage of NOX if the vibration period of the concentration of hydrocarbons longer is than a predetermined range. When hydrocarbons are being fed from the hydrocarbon feed valve within the predetermined range of amplitude and the predetermined range of period, if the amount of adsorption of hydrocarbons in the exhaust purification catalyst exceeds a predetermined judgment value of the adsorption amount, at least one of reducing amount of feed of hydrocarbons and lengthening feed interval of hydrocarbons is performed.