We report a spectrally and temporally cascaded dual-soliton Stokes excitation source for broadband coherent anti-Stokes Raman spectroscopy (CARS) based on a single Yb-doped fiber laser. The strong birefringence of a polarization-maintaining photonic crystal fiber has the potential to simultaneously generate two solitons along different eigenpolarization axes, allowing for an extra degree of freedom in tuning the properties of the supercontinuum. With well-separated spectral regions of this dual-soliton, the CARS spectral coverage can be greatly extended. Taking advantage of the dispersion characteristic of the two orthogonal polarized modes and applying identical linear frequency chirp on both soliton Stokes pulses further allows that spectral CARS information can be encoded and acquired in time. The chirped pump pulse, in conjunction with dual-soliton Stokes pulses, can potentially yield gapless coverage of Raman transitions from 800 to 1800 cm–1 with a spectral resolution of 15 cm−1. Broadband spectral coverage capability is theoretically verified with simulations and then experimentally demonstrated by CARS spectroscopy with varied polymer materials. We also demonstrate hyperspectral Raman microscopy with molecular contrast of lipid droplets. An all-fiber-based broadband excitation source may greatly simplify CARS implementation and extend the qualitative and even quantitative chemical analysis of CARS microspectroscopy.