With a highly birefringent photonic crystal fiber (HB-PCF) specially designed and fabricated in our laboratory, the two-colored solitons and small spectral component formed by the balance between the dispersion and birefringence effect are generated above 2000 nm when the polarization direction of pump pulse is aligned along the fast and slow axis of HB-PCF. When the average power of the pump at 870 nm increases from 100 to 300 mW, the broadband solitons at the fast and slow axis and small spectral component can be efficiently generated from 2120 to 2230 nm, 2070 to 2180 nm, and 2260 to 2370 nm, and the tunable wavelength range can be up to 300 nm. To the best of our knowledge, the largest span of soliton wavelength shift over 1300 nm is achieved. The widely tunable soliton pulse and small spectral component can provide the particularly useful short-pulse source for the mid-infrared photonics and spectroscopy.