A method of operating a brake redundancy device including a main braking controller and a backup braking controller, includes: confirming whether or not a command signal for deceleration of the vehicle has been received, by the backup braking controller; executing a front-wheel braking mode by the backup braking controller when the command signal has been received; determining whether or not an allowable condition for providing the hydraulic pressure to wheel cylinders of rear wheels has been satisfied; and executing a rear-wheel braking mode through a cooperative control of the main braking controller and the backup braking controller when the allowable condition has been satisfied, wherein in the executing of the rear-wheel braking mode, the hydraulic pressure is provided from the backup braking controller to a portion of the main braking controller.