The transmission spectra and defect mode properties of the one-dimensional (1D) photonic crystal with Bragg microcavity are studied, where the Bragg reflectors are composed of alternately arranged different dielectrics with positive and negative indices. The transfer matrix is expanded in Taylor series near the central frequency, and the formulae of transmission and the quality factor are obtained with the first order approximation. Frequency variance of the defect mode near the central frequency caused by change of the thickness of defect layer material (DLM) can be well explained with the method of the first order approximation. The formula of the quality factor is almost identical with the result of numerical calculation. The quality factor at the central frequency is higher, and increasing defect layer thickness and the number of period can enhance the quality factor of the defect mode.