We investigate the transmission of ultrashort pulses through impurity band-based photonic crystal waveguides. It is found that in the general case the transmission behavior depends strongly on the pulse width with respect to the resonance linewidth in impurity bands. By controlling the configuration of the waveguides, quasiflat impurity bands can be obtained in which the dependence of transmission on pulse width is very weak. As long as the pulse width is much narrower than the bandwidth, pulses can transmit through the quasiflat impurity bands with negligible distortion and attenuation. The conditions necessary for achieving quasiflat impurity bands are derived by examining waveguides of different configurations and properties. The mechanism responsible for the formation of quasiflat impurity bands is revealed from the discussion of the symmetry of single defect and their coupling.