Nonlinear transmission and supercontinuum generation with femtosecond pulse in a new designed high birefringence photonic crystal fiber are numerically simulated and analyzed by using split-step Fourier algorithm. The influences of the center wavelength, the peak power, the half-width and the polarization direction of the input pulse on supercontinuum are discussed in detail. It is shown that the supercontinuum could be broadened to an ultra-wide wavelength range of 550-2200nm. If the center wavelength of the input femtosecond pulse is close to that of the inflexion of the dispersion curves, the spectrum will be up to the widest range. The generated supercontinuum becomes wider with increasing the peak power and the pulse half-width of the input pulse. The width of the supercontinuum will become narrower if the input polarization direction gets away from both principal axis directions. Accordingly the new designed high birefringence photonic crystal fiber could be effectively applied to the generation of ultrabroadband supercontinuum.