An auxiliary device for a hydraulic brake assembly used on a two-wheel vehicle includes a body and a transmission device. The body has four cylinders respectively connected to the left and right brake lever hoses, and front and rear wheel brake hoses. By the operation of the transmission device, the front and the rear wheels are braked by either pulling the left brake lever or the right brake lever. The front wheel brake unit and the rear wheel brake unit are simultaneously activated by pulling either the left brake lever or the right break lever. The front wheel is braked right after the rear wheel is braked, and the braking force applied to the rear wheel is larger than that to the front wheel.