NOx purification method of an exhaust purification system of an internal combustion engine in which an air-fuel ratio sensor (23, 24) for detecting an air-fuel ratio of exhaust gas is arranged in an engine exhaust passage and an exhaust purification control is performed based on an air-fuel ratio detected by the air-fuel ratio sensor (23, 24), wherein the air-fuel ratio sensor is comprised of a type of sensor which has a solid electrolyte, electrodes (62, 63) respectively covering two side surfaces of the solid electrolyte, and a diffusion resistance layer covering one of electrodes (62, 63) and in which exhaust gas is guided on to the diffusion resistance layer, when the air-fuel ratio of the exhaust gas changes and the air-fuel ratio detected by the air-fuel ratio sensor (23, 24) changes, the change of the air-fuel ratio detected by the air-fuel ratio sensor (23, 24) is governed by an amount of deposition of sulfur ingredients at the air-fuel ratio sensor (23, 24), at this time, the larger the amount of deposition of sulfur ingredients at the air-fuel ratio sensor (23, 24) becomes, the smaller an amount of change of the air-fuel ratio detected by the air-fuel ratio sensor (23, 24) and the longer a time period of change of the air-fuel ratio become, and an amount of sulfur poisoning of the air-fuel ratio sensor (23, 24) is detected from the change of the air-fuel ratio detected by the air-fuel ratio sensor (23, 24) at this time, wherein an exhaust purification catalyst is arranged in the engine exhaust passage and the amount of sulfur poisoning of said exhaust purification catalyst is estimated from the change of the air-fuel ratio detected by the air-fuel ratio sensor, wherein a hydrocarbon feed valve for feeding hydrocarbons is arranged in the engine exhaust passage upstream of said exhaust purification catalyst, NO X contained in the exhaust gas and reformed hydrocarbons are made to react in said exhaust purification catalyst, precious metal catalysts (51, 52) are carried on an exhaust gas flow surface of said exhaust purification catalyst and a basic exhaust gas flow surface part is formed around said precious metal catalysts (51, 52), said exhaust purification catalyst reducing the NO X which is contained in exhaust gas if a concentration of hydrocarbons which flow into the exhaust purification catalyst is made to vibrate by within a predetermined range of amplitude and within a predetermined range of period and being increasing in storage amount of NO X which is contained in exhaust gas if the vibration period of the hydrocarbon concentration is made longer than the predetermined range, at the time of engine operation, an injection period of hydrocarbons from the hydrocarbon feed valve is controlled so that the concentration of hydrocarbons which flow into the exhaust purification catalyst vibrates by within the predetermined range of period, and an injection amount of hydrocarbons from the hydrocarbon feed valve is controlled so that the amplitude of the change of concentration of hydrocarbons which flow into the exhaust purification catalyst becomes within the predetermined range of amplitude, and wherein in said exhaust purification catalyst, NO X contained in exhaust gas and reformed hydrocarbons react whereby a reducing intermediate containing nitrogen and hydrocarbons is produced and wherein an injection period of the hydrocarbons is a period necessary for continued production of the reducing intermediate.