Conventional defect modes in all-dielectric 1D photonic crystals (PCs) are polarization-insensitive. This poses a great challenge in achieving high-performance polarization selectivity. In this Letter, we introduce a defect layer into a 1D PC containing hyperbolic metamaterials to achieve an anomalous defect mode with polarization-sensitive characteristics. As the incident angle increases, such a defect mode remains almost unshifted under transverse magnetic polarization, while strongly shifting toward shorter wavelengths under transverse electric polarization. The polarization-sensitive characteristics of the defect mode can be well explained by the Fabry-Perot resonance condition. Assisted by the polarization-sensitive defect mode, wide-angle polarization selectivity with an operating angle width up to 54.8° can be realized. Our work provides a route to designing wide-angle linear polarizers using simple 1D structures, which would be useful in liquid crystal display and Q-switched lasers.