The characteristics of propagation and polarization are given for high-birefringence fibers with single crystal as inner cladding in this article. According to the theory of optical waveguide, the dispersion equations and the cutoff characteristics are derived for ordinary light (o light) and extraordinary light (e light) under the condition of weakly guiding fibers. Simulating on computer, we can divide the characteristics plots into four areas: cutoff area, monomode single-polarization area, monomode double-polarization area and multimode area. In the monomode double-polarization area, the polarization mode dispersion characteristics are analyzed for the two polarization modes. The existent condition of monomode single-polarization area and monomode double-polarization area is also analysed. It is found that the geometrical and optical parameters (S and Rx, Ry) and the outer cladding index n3 have great influence on the divided four areas and their polarization properties. These results provide a theory foundation for the design of fiber-optifc polarizers ,and suggests a new type of optical fiber design using high-birefringence monomode fibers