We examined the effect of an antireflection (AR) coating to enhance the TM transmittance of the wire-grid polarizer. The polarization transmission spectra were calculated using the rigorous coupled-wave analysis. As a result, we verified that an AR film should be inserted between a wire-grid and a Si substrate as regards the TM transmittance and the polarization function. Based on the simulation results, we fabricated a tungsten silicide (WSi) wire-grid polarizer with SiO films on both sides of the Si substrate. The transmittance exceeded 80% at a $4–5\mathrm{\mu m}$ wavelength range, although the theoretical transmittance of Si substrate is 54% and the ratio of the TM and TE transmittances reached $24\mathrm{dB}$ at a $3\mathrm{\mu m}$ wavelength when the WSi grating has a $300\mathrm{nm}$ thickness, a $400\mathrm{nm}$ period, and a fill factor of 0.6. Wire-grid polarizers with higher transmittance and larger extinction ratio can be obtained by adjusting the AR film thickness, the fill factor, and the thickness of the WSi grating.