An exhaust purification system of an internal combustion engine which comprises: an exhaust purification catalyst in an engine exhaust passage; a hydrocarbon feed valve in the engine exhaust passage upstream of the exhaust purification catalyst; wherein precious metal catalysts are 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 catalysts; stored NO x amount calculation means for calculating the amount of NO x which is stored in the exhaust purification catalyst; first NO x removal control means for reducing NO X which is contained in an exhaust gas by making a concentration of hydrocarbons which flow into the exhaust purification catalyst periodically rich within a predetermined range of amplitude and within a predetermined range of period by controlling the injection amount and injection timing of the hydrocarbon feed valve; NO x removal control execution means for executing the first NO x removal control if the temperature of the exhaust purification catalyst exceeds a predetermined active temperature (Tm); cylinder rich control means for performing the cylinder rich control, wherein a rich air-fuel ratio combustion gas is generated in a cylinder by feeding additional fuel into the combustion chamber; and exhaust rich control means for performing the exhaust rich control, wherein hydrocarbons from the hydrocarbon feed valve are fed into the engine exhaust passage to make air-fuel ratio of the exhaust gas rich; characterized in that the exhaust purification system further comprises: rich control judgement means for performing, when the stored NO x amount exceeds a second allowable threshold, in addition to the first NO x removal control, the exhaust rich control, if a speed of a vehicle is lower than a predetermined speed and if the exhaust rich control is possible, or the cylinder rich control if the speed of the vehicle is larger than the predetermined speed and if the cylinder rich control is possible. an exhaust purification catalyst in an engine exhaust passage; a hydrocarbon feed valve in the engine exhaust passage upstream of the exhaust purification catalyst; wherein precious metal catalysts are 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 catalysts; stored NO x amount calculation means for calculating the amount of NO x which is stored in the exhaust purification catalyst; first NO x removal control means for reducing NO X which is contained in an exhaust gas by making a concentration of hydrocarbons which flow into the exhaust purification catalyst periodically rich within a predetermined range of amplitude and within a predetermined range of period by controlling the injection amount and injection timing of the hydrocarbon feed valve; NO x removal control execution means for executing the first NO x removal control if the temperature of the exhaust purification catalyst exceeds a predetermined active temperature (Tm); cylinder rich control means for performing the cylinder rich control, wherein a rich air-fuel ratio combustion gas is generated in a cylinder by feeding additional fuel into the combustion chamber; and exhaust rich control means for performing the exhaust rich control, wherein hydrocarbons from the hydrocarbon feed valve are fed into the engine exhaust passage to make air-fuel ratio of the exhaust gas rich; characterized in that the exhaust purification system further comprises: rich control judgement means for performing, when the stored NO x amount exceeds a second allowable threshold, in addition to the first NO x removal control, the exhaust rich control, if a speed of a vehicle is lower than a predetermined speed and if the exhaust rich control is possible, or the cylinder rich control if the speed of the vehicle is larger than the predetermined speed and if the cylinder rich control is possible.