The temporal and spectral properties of terrestrial gamma-ray flashes (TGFs) are studied. The delay of low energy photons relative to high energy ones in the γ-ray variations of the TGFs with high signal to noise ratio has been revealed by an approach of correlation analysis in the time domain on different time scales. The temporal structures of the TGFs in high energy band are usually narrower than that in low energy band. The spectral hardness has a general trend of decreasing with time in a flash. The observed temporal and spectral characteristics give constraints and valuable hints on the flash production mechanism.