As the optical absorption coefficient of KDP or DKDP frequency doubling crystal in an Inertial Confinement Fusion (ICF) facility effects directly its frequency conversion efficiency and output energy, this paper researches the measurement methods of the absorption coefficients for two kinds of crystals. A measurement method based on LAMBERT-BEER law was proposed under oblique incidence for frequency doubling crystals. Then, the relationship between the polarization state of incident light and the propagation of light in the crystals under oblique incidence was analyzed. An iterative algorithm for calculating extraordinary refractive index of the crystals was presented. On the basis of the iterative algorithm, the extraordinary refractive index was obtained and the optical absorption coefficient of KDP or DKDP frequency doubling crystal was calculated by using the measured dada indirectly. The error sources were analyzed in detail. It shows that total measuring error of this method is less than 0.000 2 cm-1. Finally, a 40 mm×40 mm×60 mm crystal switch was measured and the obtained results were compared with that of spectrophotometry. The comparison indicates that the deviation of the two methods is less than 0.000 2 cm-1, which verifies that the proposed method can be used in absorption coefficient measurement of KDP or DKDP frequency doubling crystal in the ICF facility.