A new type of micro-structured optical fiber (MOF) is designed. The fiber cladding has two pairs of elliptical air holes that are perpendicular to each other. The larger holes are filled with air and the smaller holes are filled with magnetic fluid. The four holes form a rectangular core. The finite element method is utilized to simulate and analyze the birefringence and confinement loss of the fiber at 2 μm wavelength band, and the best fiber structure is obtained by the structure parameters optimization. The simulation results show that the optical fiber model birefringence can reach to 10-3, while the loss is less than 10-11 dB·m-1, thus, double standards of high birefringence and low confinement loss are achieved simultaneously. The refractive index of the magnetic fluid material can be changed by change of the external magnetic field, and then the effective refractive index of the fiber is changed. Consequently, the transmission of polarized light in the fiber can be tuned continuously.