We estimated the seismic attenuation (Q factor) of the Greenland Ice Sheet (GrIS) by comparing observed and theoretical Rayleigh waveforms. Observed waveforms are obtained by interfering with noise waveforms in vertical-component seismograms between stations, which belong to the latest broadband seismic network distributed throughout Greenland (GLISN network). Theoretical waveforms are calculated by parallel computation with the latest 3-D seismic waveform modeling. Comparing the observed waveforms with the theoretical waveforms at different Q factors reveals that GrIS has a low Q of Q_P, Q_S ≤ 50, indicating very high attenuation of seismic waves due to the ice. This study is the first to confirm the low Q factor of ice sheets via ultra-long-distance propagation (~several hundreds to 1,000 km). The Q factors obtained in this study are indispensable for estimating the thermal status of GrIS, as well as for interpreting the characteristics of seismic waveform that propagates through GrIS.