A widely used polarizer in the IR is the wire-grid polarizer. Wire-grid polarizers with a typical minimal wire spacing of ~0.25 microm perform well in the middle IR and the far IR, but in the near IR the performance deteriorates as the wavelength approaches the wire spacing. A possibility for improving this performance is to put two wire grids in tandem with their transmission axes parallel. Starting with the extended Mueller matrix description for a single wire grid, we present a mathematical treatment of this tandem polarizer showing that performance improves quadratically; e.g., a single polarizer extinction ratio of 100 increases to a tandem extinction of 10,000. The improved performance is also verified experimentally.