The calculated formula of equivalent refractive index N* of non-symmetrical three-layer period (a b c) has been derived in this papsr. The formula has been used for the design of anti-reflection coatings in infrared. The calculated and experimental results are given in the paper. The average transmisson of the coatings is 98 in the response wave region of InSb (3~5μm) detector and HgCdTe (8~12μm) detector. The average transmission of the coatings is greater than or equal to 94% in 2~13 μm, 3~14μm and 3.5~15 μm. Especially in 11 μm wavelength region (3.8~14.8 μm), the minimum transmission of the coatings is greater than or equal to 90%.