In this paper, the absorption spectra characters of the (Cr, Yb): YAG, Cr:YAG and Yb:YAG crystals are reported. In the absorption spectra of the (Cr, Yb): YAG crystal, there are two absorption bands at 937 nm and 968 nm respectively, which are suitable for InGaAs diode laser pumping; and there is an absorption band of Cr4+ near 1030 nm, which is suitable for passive Q switch laser output at 1.03 micrometers . This Cr-Yb-codoped crystal may be a potential material for compact, efficient, high-stable diode laser pumped passive Q-switched solid-state laser.