An exhaust purification system for an internal combustion engine, comprising: an exhaust purification catalyst arranged in an engine exhaust passage; a hydrocarbon feed valve arranged in the engine exhaust passage upstream of the exhaust purification catalyst; a precious metal catalyst being carried on an exhaust gas flow surface of the exhaust purification catalyst; a basic layer provided around the precious metal catalyst; and an electronic control unit configured to: perform a first NO x removal method which reduces NO x contained in an exhaust gas by a reducing intermediate, the reducing intermediate being held on the basic layer and generated by injecting hydrocarbons from the hydrocarbon feed valve within a predetermined range of period, perform a second NO x removal method in which an air-fuel ratio of the exhaust gas flowing into the exhaust purification catalyst is made rich by a period which is longer than the predetermined range to make NO x which was stored in the exhaust purification catalyst when the air-fuel ratio of the exhaust gas was lean be released from the exhaust purification catalyst and be reduced, switch an NO x removal method from the second NO x removal method to the first NO x removal method when a temperature of the exhaust purification catalyst rises and the temperature exceeds a predetermined switching temperature, and control the predetermined switching temperature in accordance with an amount of NO x in the exhaust gas flowing into the exhaust purification catalyst, which amount of NO x changes in accordance with an engine operating state, the predetermined switching temperature being made lower if the amount of NO x in the exhaust gas flowing into the exhaust purification catalyst increases at least when the amount of NO x in an inflowing exhaust gas is in a range of change at a small amount side within a range of change of the amount of NO x in the inflowing exhaust gas. an exhaust purification catalyst arranged in an engine exhaust passage; a hydrocarbon feed valve arranged in the engine exhaust passage upstream of the exhaust purification catalyst; a precious metal catalyst being carried on an exhaust gas flow surface of the exhaust purification catalyst; a basic layer provided around the precious metal catalyst; and an electronic control unit configured to: perform a first NO x removal method which reduces NO x contained in an exhaust gas by a reducing intermediate, the reducing intermediate being held on the basic layer and generated by injecting hydrocarbons from the hydrocarbon feed valve within a predetermined range of period, perform a second NO x removal method in which an air-fuel ratio of the exhaust gas flowing into the exhaust purification catalyst is made rich by a period which is longer than the predetermined range to make NO x which was stored in the exhaust purification catalyst when the air-fuel ratio of the exhaust gas was lean be released from the exhaust purification catalyst and be reduced, switch an NO x removal method from the second NO x removal method to the first NO x removal method when a temperature of the exhaust purification catalyst rises and the temperature exceeds a predetermined switching temperature, and control the predetermined switching temperature in accordance with an amount of NO x in the exhaust gas flowing into the exhaust purification catalyst, which amount of NO x changes in accordance with an engine operating state, the predetermined switching temperature being made lower if the amount of NO x in the exhaust gas flowing into the exhaust purification catalyst increases at least when the amount of NO x in an inflowing exhaust gas is in a range of change at a small amount side within a range of change of the amount of NO x in the inflowing exhaust gas. perform a first NO x removal method which reduces NO x contained in an exhaust gas by a reducing intermediate, the reducing intermediate being held on the basic layer and generated by injecting hydrocarbons from the hydrocarbon feed valve within a predetermined range of period, perform a second NO x removal method in which an air-fuel ratio of the exhaust gas flowing into the exhaust purification catalyst is made rich by a period which is longer than the predetermined range to make NO x which was stored in the exhaust purification catalyst when the air-fuel ratio of the exhaust gas was lean be released from the exhaust purification catalyst and be reduced, switch an NO x removal method from the second NO x removal method to the first NO x removal method when a temperature of the exhaust purification catalyst rises and the temperature exceeds a predetermined switching temperature, and control the predetermined switching temperature in accordance with an amount of NO x in the exhaust gas flowing into the exhaust purification catalyst, which amount of NO x changes in accordance with an engine operating state, the predetermined switching temperature being made lower if the amount of NO x in the exhaust gas flowing into the exhaust purification catalyst increases at least when the amount of NO x in an inflowing exhaust gas is in a range of change at a small amount side within a range of change of the amount of NO x in the inflowing exhaust gas.