We report on a new kind of highly birefringent and highly nonlinear photonic crystal fiber with a row of sub-micron air hole in the fiber core. The diameters of air holes in fiber core and cladding are 0.2 μm and 6.6 μ$m respectively. The parameters of birefringence, nonlinear and dispersion coefficient of the fiber are simulated by finite element method. It is found that the birefringence of the fiber can exist at the wavelengths up to 1550 nm, which is one order of magnitude higher than that of the traditional polarization-maintaining fiber. The zero-dispersion wavelengths of the fast axis and slow axis are 1050 nm and 1080 nm respectively. This fiber has a clear advantage over conventional fiber in continuum generation. Firstly, the polarization state of the pulse traveling in the fiber can be sustained along the fiber length and the extinction ratio is more than 20 dB. In addition, the pulses travel at different group velocities along the two polarization directions, which provide a convenient way of tuning the properties of the generated supercontinuum. Using this fiber as a nonlinear medium, an efficient generation of a tunable supercontinuum is demonstrated by pumping with 15 ps pulses of 1040 nm laser radiation, which is located in the normal dispersion region. A half-wave plate is used to vary the input polarization of the light pulse launched into the fiber, and the polarization of output supercontinuum is adjusted by a Glan prism at the same time. It is experimentally found that the polarization of pulse has a significant influence on the generation of the supercontinuum. When the linear polarization of the input pulse matches with the direction of the main axis of the fiber, the supercontinuum can be broadened over wavelength range of 800-1500 nm, and the extinction ratio is 21.2 dB. The polarization direction of the output SC is found to coincide with the pump pulse. When the angle between the polarization of the input pulse and the fast axis is increased to 45 degrees, the output supercontinuum is circularly polarized and becomes narrowest, extending from 900 to 1300 nm. So we can realize the wide tuning of a supercontinuum by only changing the polarization direction of the incident pulse. Under the circumstances, the pulse in optical fiber can be broken into two components along the main axis respectively. If the input polarization direction is away from both principal axis directions, the power along the main axis and the contribution of cross phase modulation are reduced because of the walk-off effect, so the width of the supercontinuum will become narrower. It is suggested that this type of high birefringence photonic crystal fiber could be effectively applied to the generation of the tunable supercontinuum.