In this paper, we consider the track-following control problem in the optical data storage systems in the presence of the eccentricity. The eccentricity results in the radial deviation of the objective lens so that it degrades the reliability of the data decoding system. To cope with the eccentricity, an adaptive disturbance compensation technique is newly proposed in the time domain based on a disturbance observer of reduced order, which effectively estimates the low frequency components of the disturbance. The proposed compensator is simply added to the conventional feedback control. The error dynamics of the observer and the sensitivity analysis are given to illustrate the effectiveness of the proposed approach. Finally, through experiments in an optical storage system, the feasibility of the proposed approach is verified.