Disturbance observer based control system, which utilizes estimated disturbance to compensate the influence of real disturbance, is widely applied in industrial systems. In this article, a frequency response data based auto-tuning method is proposed to design a bandwidth-optimized disturbance observer. The identification of a nominal plant model and the design of a low-pass filter are accomplished simultaneously in the discrete domain. This significantly reduces the design effort required in existing parametric model-based and experience-based methods. A convex optimization problem is formulated by converting all the original constraints into convex form to save calculation time. Finally, the efficacy of the proposed method is verified by comparing the experimental results of existing methods with those of the proposed method in a nonminimum phase motion stage.