In a Guest-Host cell the orientational ordering of dyes doped into liquid crystals has been investigated. To evaluate the influence of the host liquid crystals on the ordering of the dyes we have measured precisely the ordering parameters of the liquid crystals by using the dichroic ratio of the absorbances for infrared light polarized parallel and perpendicular to the diector. Our experimental results show that the ordering of the dyes can be expressed as a function of not only the molecular structure of the dyes but also the order parameter of the liquid crystals. These functions are dependent on the kinds of the liquid crystals and the dyes. Particularly the combination such as anthraquinone dyes doped into cyanobiphenyl liquid crystals show a very high ordering parameter. This is considered due to a strong intermolecular interaction between the dipoles of both liquid crystals and dyes.