We present an approach for bandwidth-adjustable optical filter with the dynamic grating in erbium-doped fiber (EDF). The dynamic grating is introduced by the interference of two coherent light beams counter-propagating in the pumped EDF per the phenomenon of gain saturation. The bandwidth of the grating is determined by the length of the grating, i.e., the length of the interference region. With the technique of synthesis of optical coherence function (SOCF), we localize the interference into a range at an arbitrary position along the fiber by modulating the frequency of the two interfering light beams. The length of the range is controlled by adjusting the frequency modulation parameter. In this way, the length of the dynamic grating is controlled and its reflection bandwidth then adjusted. The experimental demonstration is given.