An internal combustion engine comprising: a cylinder fuel injector configured to inject fuel to an inside of a combustion chamber; an exhaust purification catalyst which is arranged in an engine exhaust passage; a secondary air feed device which feeds air to the engine exhaust passage at an upstream side from the exhaust purification catalyst; a related temperature acquisition device which acquires a related temperature which is a temperature of a part with which a temperature of the exhaust purification catalyst is linked; and a control device; wherein the control device is configured to perform first catalyst warm-up control and second catalyst warm-up control which promote a rise in temperature of the exhaust purification catalyst, the first catalyst warm-up control includes control which injects fuel from the cylinder fuel injector in a compression stroke to make a fuel concentration around an ignition device rise which retards an ignition timing to make a temperature of an exhaust gas which flows out from the combustion chamber rise, the second catalyst warm-up control includes control which feeds air to the engine exhaust passage to make components which are included in the exhaust gas oxidize and make the temperature of the exhaust gas rise, characterized in that a first temperature range of the related temperature at which the first catalyst warm-up control is performed and a second temperature range of the related temperature at which the second catalyst warm-up control is performed are preset in the control device, and the second temperature range is set so as to be included inside the first temperature range and a range of performance of the first catalyst warm-up control is set broader than a range of performance of the second catalyst warm-up control. a cylinder fuel injector configured to inject fuel to an inside of a combustion chamber; an exhaust purification catalyst which is arranged in an engine exhaust passage; a secondary air feed device which feeds air to the engine exhaust passage at an upstream side from the exhaust purification catalyst; a related temperature acquisition device which acquires a related temperature which is a temperature of a part with which a temperature of the exhaust purification catalyst is linked; and a control device; wherein the control device is configured to perform first catalyst warm-up control and second catalyst warm-up control which promote a rise in temperature of the exhaust purification catalyst, the first catalyst warm-up control includes control which injects fuel from the cylinder fuel injector in a compression stroke to make a fuel concentration around an ignition device rise which retards an ignition timing to make a temperature of an exhaust gas which flows out from the combustion chamber rise, the second catalyst warm-up control includes control which feeds air to the engine exhaust passage to make components which are included in the exhaust gas oxidize and make the temperature of the exhaust gas rise, characterized in that a first temperature range of the related temperature at which the first catalyst warm-up control is performed and a second temperature range of the related temperature at which the second catalyst warm-up control is performed are preset in the control device, and the second temperature range is set so as to be included inside the first temperature range and a range of performance of the first catalyst warm-up control is set broader than a range of performance of the second catalyst warm-up control.