The objective of the present invention is to provide an exhaust purification system that is capable of purifying exhaust gas during both lean and stoichiometric driving. The exhaust purification system is equipped with: a feedback-use identifier, which identifies parameter values such that the error between the output value from a LAF sensor and the estimated value for the LAF sensor output as obtained from a model equation is minimized; and a stoichiometric driving mode controller. The controller performs feedback control and thereby determines the fuel injection amount such that in the stoichiometric driving mode the equivalence ratio value as calculated from the parameters reaches a target value which is set such that a three-way purification reaction occurs in an under-engine catalyst. The identifier identifies the model parameters before feedback control is initiated by the controller.