The photonic crystal combining with two single negative dispersive materials (one is negative permittivity and positive
permeability, the other is negative permeability and positive permittivity) is considered and it's dispersive and
transmission properties are studied theoretically. We show that this structure can possess a new type of photonic bandgap
at the frequencies where the materials electric permittivity or magnetic permeability is zero. With the different ways of
traditional Bragg bandgap and zero equivalent refractive index bandgap, the new bandgap decided by the dispersive
characteristics of the materials, and this band gap distinguished itself from above two bandgaps in that it is sensitive to
polarization mode of incidence wave and is scale-length invariant and robust against disorder. The difference of these
bandgaps and the use of SNG dispersive material in gradual periodic photonic crystal are discussed.