An ISG vehicle system may include an alternator supplying electric power of a vehicle and alternating engine power to electrical energy, a battery storing the electric power of the vehicle, an alternator supplying electric power of a vehicle and alternating engine power to electrical energy, a V2X controller receiving external infrastructure information and determining vehicle location, an ISG controller obtaining the external infrastructure information and the vehicle location through communication with the V2X controller and obtaining the status of the battery and charge amount information through communication with the battery sensor to determine operable time of ISG (Idle Stop and Go) function of the vehicle and whether the ISG function operates, and an engine controller receiving operation signal of the ISG function through communication with the ISG controller to determine whether the engine operates.