Terahertz filters with dual-band and sharp slope rate of edge characteristics are reported. We realize the change from single band to dual-band by adding a SRR to the original structure. The mechanism for the dual-band is attributed to introducing a new resonance point. The slope rates of edges for two stop-bands are 297dB/THz, 297 dB/THz, 287 dB/THz, and 354 dB/THz. Tuning bandwidths and center frequencies can be realized by modulating the main parameters of the structure. Besides, the filter is insensitive to the polarization of the THz radiation under g=0 m.