Wire-grid polarizers (WGPs) have been widely used in various fields, such as polarimetry, imaging, display, spectroscopy, and optical isolation. However, conventional WGPs used in diverse mid-wavelength infrared (MWIR) applications show high reflection losses, which intrinsically arise from high refractive indices of their IR-transmitting substrates, such as silicon (Si) and germanium (Ge). This study demonstrated the enhanced transmittance of a transverse magnetic (TM) wave that surpassed ~80% over the entire MWIR range from 3000 to 5000 nm in a narrow air gap of a WGP, where aluminum (Al) was selectively deposited on a nanopatterned Si substrate using an oblique angle deposition method. Moreover, a higher TM wave transmittance was achieved by reducing the air gaps of the WGPs in the nanopatterns, which were distinctly different from the traditional WGPs comprising metal wires patterned directly on a flat substrate. A finite-difference time-domain simulation was performed to investigate optical properties of the proposed WGPs, which showed that the electric field in the air nanogap was remarkably enhanced. The characteristic performances were further investigated using a combination of an effective medium approximation and an admittance diagram, revealing that the broadband transmission enhancement could be attributed to a combined effect of a strong electric field and a better admittance matching. The approach and results described in this paper hold promise for the design and the fabrication of high-quality WGPs, as well as their numerous applications.