The spectral and luminescence properties of (Cr4+, Yb3+):YAG crystal, and the absorption spectra of Cr4+:YAG crystal and Yb3+:YAG crystal are reported. In the absorption spectra of (Cr4+, Yb3+):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 a absorption band of Cr4+ at 1030 nm, which is suitable for passive Q-switched laser output at 1030 nm. This (Cr4+, Yb3+)-codoped YAG crystal may be a promising material for compact, efficient and high-stable diode laser pumped solid-state passive Q-switched laser.