We have performed ToO observations for three bright GRBs with the Japanese X-ray satellite Suzaku. Suzaku strongly supports the follow-up observations by Swift, especially in the late time afterglow phase, with its capabilities of larger effective area and wider energy band compared with Swift/XRT. In this presentation, mainly focusing on the X-ray afterglow of GRB 060904A, we introduce these ToO observation results. In GRB 060904A, we found rapid spectral softening with the photon indices from 1.5 to 5.3 during the steep decay (prompt tail) phase in the BAT and XRT data. This ultra soft spectra suddenly disappeared at the transition time from the prompt tail phase to the shallow decay one. After that, typical afterglow spectra with the photon indices of 2.0 are continuously and preciously monitored by both XRT and Suzaku/XIS up to 1 day since the burst trigger time. To explain this ultra soft spectra, we introduce a spectral cutoff model instead of power-law, and investigate the possibility of the maximum energy of electron distribution. We could successfully trace the temporal history of cutoff energy and it shows the time dependence of ∝t-3∼t-4 while the following afterglow spectra are quite stable. This fact indicates that the emitting material of prompt tail is due to completely different dynamics from the shallow decay component. Therefore we conclude the emission sites of two distinct phenomena obviously differ from each other.