An exhaust purification system for an internal combustion engine which has a plurality of cylinders, said exhaust purification system comprising: an exhaust purification catalyst configured to be arranged in an engine exhaust passage and capable of storing oxygen; a downstream side air-fuel ratio sensor which is arranged at a downstream side of the exhaust purification catalyst in a direction of flow of exhaust; and a control device for controlling an average air-fuel ratio of exhaust gas which flows into the exhaust purification catalyst and combustion air-fuel ratios when combustion is performed in the cylinders, wherein the control device is configured to: perform average air-fuel ratio control which controls the average air-fuel ratio for all cylinders alternately between a rich air-fuel ratio which is richer than a stoichiometric air-fuel ratio and a lean air-fuel ratio which is leaner than the stoichiometric air-fuel ratio and when the temperature of the exhaust purification catalyst is lower than a predetermined first switching temperature, perform inter-cylinder air-fuel ratio control which individually controls the combustion air-fuel ratio of each of the cylinders so that the combustion air-fuel ratio of at least one cylinder among the plurality of cylinders matches the rich air-fuel ratio, even when the average air-fuel ratio is controlled to the lean air-fuel ratio by the average air-fuel ratio control; and control the average air-fuel ratio in the average air-fuel ratio control when the temperature of the exhaust purification catalyst is lower than a predetermined second switching temperature, so that a lean shift amount, which is a difference between the average air-fuel ratio and stoichiometric air-fuel ratio when controlling the average air-fuel ratio to a lean air-fuel ratio, becomes smaller than a rich shift amount, which is a difference between the average air-fuel ratio and stoichiometric air-fuel ratio when controlling the average air-fuel ratio to a rich air-fuel ratio, and control the average air-fuel ratio in the average air-fuel ratio control when the temperature of the exhaust purification catalyst is the second switching temperature or more, so that the lean shift amount becomes larger than the rich shift amount. an exhaust purification catalyst configured to be arranged in an engine exhaust passage and capable of storing oxygen; a downstream side air-fuel ratio sensor which is arranged at a downstream side of the exhaust purification catalyst in a direction of flow of exhaust; and a control device for controlling an average air-fuel ratio of exhaust gas which flows into the exhaust purification catalyst and combustion air-fuel ratios when combustion is performed in the cylinders, wherein the control device is configured to: perform average air-fuel ratio control which controls the average air-fuel ratio for all cylinders alternately between a rich air-fuel ratio which is richer than a stoichiometric air-fuel ratio and a lean air-fuel ratio which is leaner than the stoichiometric air-fuel ratio and when the temperature of the exhaust purification catalyst is lower than a predetermined first switching temperature, perform inter-cylinder air-fuel ratio control which individually controls the combustion air-fuel ratio of each of the cylinders so that the combustion air-fuel ratio of at least one cylinder among the plurality of cylinders matches the rich air-fuel ratio, even when the average air-fuel ratio is controlled to the lean air-fuel ratio by the average air-fuel ratio control; and perform average air-fuel ratio control which controls the average air-fuel ratio for all cylinders alternately between a rich air-fuel ratio which is richer than a stoichiometric air-fuel ratio and a lean air-fuel ratio which is leaner than the stoichiometric air-fuel ratio and when the temperature of the exhaust purification catalyst is lower than a predetermined first switching temperature, perform inter-cylinder air-fuel ratio control which individually controls the combustion air-fuel ratio of each of the cylinders so that the combustion air-fuel ratio of at least one cylinder among the plurality of cylinders matches the rich air-fuel ratio, even when the average air-fuel ratio is controlled to the lean air-fuel ratio by the average air-fuel ratio control; and control the average air-fuel ratio in the average air-fuel ratio control when the temperature of the exhaust purification catalyst is lower than a predetermined second switching temperature, so that a lean shift amount, which is a difference between the average air-fuel ratio and stoichiometric air-fuel ratio when controlling the average air-fuel ratio to a lean air-fuel ratio, becomes smaller than a rich shift amount, which is a difference between the average air-fuel ratio and stoichiometric air-fuel ratio when controlling the average air-fuel ratio to a rich air-fuel ratio, and control the average air-fuel ratio in the average air-fuel ratio control when the temperature of the exhaust purification catalyst is the second switching temperature or more, so that the lean shift amount becomes larger than the rich shift amount.