P>We developed a method for estimating the seismic-wave attenuation (1/Q) in a seismically active region such as an aftershock area. To estimate the attenuation factor between two adjacent hypocentres, we employed two seismograms recorded at a station and calculate the ratio between two power spectra of direct waves normalized by those in the coda for both the events. The coda normalization of the spectrum and the ratio between the two events minimize the possible influences of sources, sites, instruments and attenuation from the station to the hypocentral area. The 1/Q value can be estimated from the variation of the ratios of event pairs calculated at many stations for various traveltime differences between the even pairs. This method involves double-difference (DD) estimation from the logarithmic power spectra for estimating the 1/Q structure, employing a concept similar to the recently developed 'DD tomography' for velocity structures. We applied this method to the aftershock area of the 2005 West Off Fukuoka Prefecture Earthquake (M7.0) in order to investigate the 1/Q structure of P waves. By using the spectra of the seismograms of 1781 events recorded at a dense seismic network deployed around the aftershock area, we obtained the spatial variation of the 1/Q value in this region. The 1/Q distribution thereby obtained suggests that there exists a high-attenuation region around the edge of the main shock fault, which could correspond to the segment boundary between the earthquake fault and the adjacent faults. In addition, we found that the initiation points of the main shock and aftershocks were located in a low-attenuation region.