Polarizer, as an indispensable optical element, has been widely used in various optical systems, which splits a beam into two beams of orthogonal linear polarizations. Due to the appearance of the vector optical field (VOF) and its unique properties, the vector polarizer also meets the requirement in a wide variety of applications. Here we present and demonstrate the realization of dielectric broadband vector polarizer, being in fact a liquid-crystal-based space-variant uniaxial crystal (LC-SV-UAC), which is made by a wedged thin cell adhered with space-variant photo-aligned dichroic dye films and filled with the nematic liquid crystal with a thickness of tens of microns. The vector polarizer works based on the birefringent mechanism to spatially separate the orthogonally polarized ordinary and extraordinary beams. The vector polarizers via a LC-SV-UAC have the advantages of mass-production and easy fabrication of large-size and complex structures. In particular, the high-performance broadband vector polarizers we presented and fabricated can not only flexibly tailor the polarization structures and the intensity patterns of optical fields but also act as a high-efficiency generator of VOF, and a key element for realizing the VOF laser and for fabricating the novel photon states in the future.