Silver is proposed as a useful metal for thin metal-film subwavelength-grating polarizers in both the terahertz and mid-infrared regions. A triangular Ag-film grating for a terahertz-region polarizer fabricated on a resin substrate showed measured TE-wave losses of higher than 45 dB in the frequency range of 0.5-2.2 THz, while TM-wave losses were lower than 0.75 dB in the range of 0.5-3THz. A triangular double Ag-film grating structure on a thin silicon substrate with an anti-reflection layer on its reverse side was fabricated for the polarizer in the mid-infrared region. Measured TE-wave losses were higher than 27 dB in the wavelength range of 16-21 μm, while the minimum TM-wave loss was 3.5 dB at around the wavelength of 19 μm. Silver films are confirmed to be promising candidates for fabricating high-performance polarizers in the terahertz and mid-infrared regions.