The refractive index sensing characteristics of the polarization maintaining (PM) microstructured optical fiber (MOF) chirped grating was systematically investigated based on finite element method (FEM) and transfer matrix method (TMM). The chirp Bragg grating reflection spectrum was numerically analyzed with the fiber air holes injected with different refractive index medium, and the relation between the reflection spectrum area and the analyte refractive index is discussed here. The analysis results show that when the analyte refractive index increases, the reflection spectrum area will be reduced; and the detection demodulation is simplified with the light intensity demodulation. Moreover, the dependence of the reflection spectrum on the center big holes size, the chirp coefficient and the site function was studied. Since two polarization modes respond similarly to the outside perturbation, the fiber possesses high stability. The results provide the theoretical basis for the application of PM-MOF grating in the optical fiber refractive index sensor and the optical fiber label-free biosensing.