fiber Bragg grating with cladding made of uniaxial crystal material whose optical axis is parallel to the axis of fiber Bragg grating was proposed. The ratio (Kcl) of the extraordinary to the ordinary ray refractive index was introduced and the influence of parameter Kcl upon the reflectivity γ, Bragg wavelength λB, the bandwidth of reflected wave △λ and the dispersion dq of this kind of fiber Bragg grating was examined using coupled-mode theory. The calculated results indicate that parameter Kcl has a strong impact on the characteristics of this kind of fiber Bragg grating, and the degrees of such impact are closely related to the values of parameter Kcl. This means Kcl can lead to the variation of Bragg wavelength while keeping its length, periodicity and the other parameters as constants. The fiber Bragg gratings using two kinds of uniaxial crystal material as cladding were discussed, respectively.