By using transfer-matrix method, optical properties of defect modes in one-dimensional photonic crystal containing a single defect layer with negative refractive index are studied. It is found that when the thickness of defect is increased, the frequency of defect modes can be changed presenting several stages. First stage is monotonously increased, second stage is a transitional process, and the third is monotonously decreased. These properties are different from those of the structure that defect layer has positive refractive index. Though the third stage is somewhat alike, but now defect modes move with greater speed. It is also found that in the whole process defect modes move faster than them in the structure containing a defect layer with positive refractive index.