Taking account the earth Q effect (i.e., frequency-dependent amplitude decay and velocity dispersion) during seismic migration simultaneously, the resultant seismic image is expected to be high resolution with true amplitude and correct timing. We present here a stabilized algorithm for such a migration incorporating inverse Q filtering scheme, so that the imaging technique is applicable to seismographs with long recording time. The earth model is assumed to be 1-D with continuous variations vertically in velocity and attenuation, and the imaging algorithm is implemented easily and efficiently in the frequency-wavenumber domain. Although such a 1-D model suits mostly to the cases in lithospheric-scale regional geophysics, it is sometimes also suitable to the exploration seismic studies. The method is demonstrated using a real data example from exploration seismics with an attempt to recover a target reflection underneath a group of strong coal-seam reflections.