In the big-data era, requirements for storage capacity and access speed in modern Hard Disk Drive (HDD) systems are becoming more and more stringent. As the track density of HDDs increases, vibration suppression of the recording arm in HDDs is becoming more challenging. Vibrations in modern HDDs are environment/product-dependent with different frequency characteristics. Furthermore, they can occur at very high frequencies with wide spectral peaks. This paper presents an adaptive algorithm to identify and suppress these high-frequency wide-spectrum vibrations. We design a vibration-compensation controller based on an adaptive disturbance observer (DOB), and devise parameter adaptation algorithms not only for the vibration frequencies but also for the spectral peak widths of the vibration. The peak-width parameters are adaptively tuned online to maximally attenuate the vibration with minimal error amplifications at other frequencies. The proposed algorithm is verified by simulations of HDDs for the problem of suppressing high-frequency wide-spectrum vibrations.