An exhaust purification system for an internal combustion engine, in which an exhaust purification catalyst is arranged in an engine exhaust passage and a hydrocarbon feed valve is arranged upstream of the exhaust purification catalyst in the engine exhaust passage, a precious metal catalyst is carried on an exhaust gas flow surface of the exhaust purification catalyst and basic exhaust gas flow surface parts are formed around the precious metal catalyst, wherein the exhaust purification catalyst has the property of reducing NO X which is contained in exhaust gas if a concentration of hydrocarbons which flow into the exhaust purification catalyst is made to vibrate at an amplitude within a predetermined range of amplitude and with a period within a predetermined range of period and has the property of a storage amount of NO X which is contained in exhaust gas increasing if a vibration period of the hydrocarbon concentration is made longer than the predetermined range of period, wherein: the system is configured to perform a first NO X purification method, the first NO x purification method being configured to purify NO x which is contained in the exhaust gas by injecting hydrocarbons from the hydrocarbon feed valve with a period within the predetermined range of period, wherein a particulate filter for trapping particulate matters in the exhaust gas is further arranged in the engine exhaust passage, characterised in that the system is configured to, if temperature increasing control should be performed when the first NO X purification method is being performed, perform injection of hydrocarbons for the first NO X purification method with the period within the predetermined range of period, and perform injection of hydrocarbons for temperature increasing control in a time period when injection of hydrocarbons for the first NO X purification method is not performed, the temperature increasing control being configured to increase a temperature of the particulate filter to remove particulate matters trapped on the particulate filter, and wherein an amount of hydrocarbons per one injection of hydrocarbons for temperature increasing control when an actual temperature of the particulate filter is low is set larger than that when the actual temperature of the particulate filter is high. the system is configured to perform a first NO X purification method, the first NO x purification method being configured to purify NO x which is contained in the exhaust gas by injecting hydrocarbons from the hydrocarbon feed valve with a period within the predetermined range of period, wherein a particulate filter for trapping particulate matters in the exhaust gas is further arranged in the engine exhaust passage, characterised in that the system is configured to, if temperature increasing control should be performed when the first NO X purification method is being performed, perform injection of hydrocarbons for the first NO X purification method with the period within the predetermined range of period, and perform injection of hydrocarbons for temperature increasing control in a time period when injection of hydrocarbons for the first NO X purification method is not performed, the temperature increasing control being configured to increase a temperature of the particulate filter to remove particulate matters trapped on the particulate filter, and wherein an amount of hydrocarbons per one injection of hydrocarbons for temperature increasing control when an actual temperature of the particulate filter is low is set larger than that when the actual temperature of the particulate filter is high.