Recently two kinds of artificial structures, namely photonic crystal and left-handed material, have potential applications in the control of light. One of the artificial structures is photonic crystal which has periodic structure array of dielectric material. The photonic crystal shows band gap structure for the wave and it can be used as potential optical devices. Another structure is the left-handed material. The left-handed materials with simultaneous negative permittivity and negative permeability possess a number of unusual electromagnetic effects. Transfer matrix method is used to analyze the transmission spectra of one-dimensional photonic crystals with negative refractive index material and positive refractive index material alternant structure. The bang gaps and dispersive relation of one-dimensional photonic crystals are analyzed. The general Bragg gaps and the resonant gap of low frequency exist in the photonic crystal. Not only the nonlocalized modes are found in such a disordered system, but also the localization states with short localization length can be easily realized due to the existence of the low frequency resonant gap.