By using the transfer matrix method, the defect modes of one-dimensional photonic crystals composed of single-negative materials are investigated. The transmission peaks in band gaps shift to the low-frequency side with the increase of the layer thickness of the air defect layer, which accords with the properties of the photonic crystals composed of traditional positive materials. However, the position of the peak is found to be insensitive to the incident angle as well as polarization of the incident light, which implies the formation of the peak cannot be contributed to the Bragg effect, but the phase elimination effect. The results show that the structure is different from the structures composed of pure positive or negative materials. These properties of the structure show the potential application of omnidirectional tunable photonic filters.