Disclosed herein are an electronic parking brake system for a vehicle and a method of driving the system, which are capable of stopping the vehicle when the operation of a vehicle service brake is impossible during the travel of the vehicle. The electronic parking brake system for the vehicle includes a controller that stores a control value of a parking brake for decelerating the vehicle to a target deceleration and outputs a braking command including the control value of the parking brake, and an electronic parking brake that generates a clamping force based on a braking command inputted from the controller.