An exhaust gas purification system for a vehicle disposed on an exhaust pipe that is connected to an exhaust side of an engine for purifying an exhaust gas of the engine, the system comprising: a housing disposed on the exhaust pipe so as to receive the exhaust gas discharged from the engine and to exhaust the exhaust gas passed rearward; a front end catalyst disposed in the housing to primarily purify the exhaust gas flowing into the housing through a front end of the housing; a rear end catalyst disposed in the housing to secondarily purify the exhaust gas passing through the front end catalyst before the exhaust gas flows out to a rear end of the housing; and a controller connected to the exhaust pipe at a front end of the housing to control a concentration of unburned fuel contained in the exhaust gas flowing into the housing, wherein the controller is configured to: perform lean control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing to be fuel lean after the engine starts, terminate the lean control at a set temperature corresponding to a maximum oxygen storage capacity according to a degree of deterioration of the front end catalyst and the rear end catalyst, perform normal control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing such that a fuel lean condition a the fuel rich condition periodically alternately repeat, terminate the lean control if the front end catalyst and the rear end catalyst are deteriorated products when the temperature of the exhaust gas flowing into the housing reaches 400°C corresponding to a maximum oxygen storage capacity in case of deteriorated products, perform oxygen purge on the front end catalyst and the rear end catalyst after the lean control ends, before performing the normal control, and perform the oxygen purge to control the oxygen saturation in the OSC material of the front end catalyst and the rear end catalyst to less than 40%. a housing disposed on the exhaust pipe so as to receive the exhaust gas discharged from the engine and to exhaust the exhaust gas passed rearward; a front end catalyst disposed in the housing to primarily purify the exhaust gas flowing into the housing through a front end of the housing; a rear end catalyst disposed in the housing to secondarily purify the exhaust gas passing through the front end catalyst before the exhaust gas flows out to a rear end of the housing; and a controller connected to the exhaust pipe at a front end of the housing to control a concentration of unburned fuel contained in the exhaust gas flowing into the housing, wherein the controller is configured to: perform lean control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing to be fuel lean after the engine starts, terminate the lean control at a set temperature corresponding to a maximum oxygen storage capacity according to a degree of deterioration of the front end catalyst and the rear end catalyst, perform normal control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing such that a fuel lean condition a the fuel rich condition periodically alternately repeat, perform lean control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing to be fuel lean after the engine starts, terminate the lean control at a set temperature corresponding to a maximum oxygen storage capacity according to a degree of deterioration of the front end catalyst and the rear end catalyst, perform normal control to control the concentration of the unburned fuel contained in the exhaust gas flowing into the housing such that a fuel lean condition a the fuel rich condition periodically alternately repeat, terminate the lean control if the front end catalyst and the rear end catalyst are deteriorated products when the temperature of the exhaust gas flowing into the housing reaches 400°C corresponding to a maximum oxygen storage capacity in case of deteriorated products, perform oxygen purge on the front end catalyst and the rear end catalyst after the lean control ends, before performing the normal control, and perform the oxygen purge to control the oxygen saturation in the OSC material of the front end catalyst and the rear end catalyst to less than 40%.