The high-average-power solid-state-laser (HAP SSL) crystal (Cr4+,Nd3+)∶Gd3Ga5O12 [(Cr4+,Nd3+)∶GGG] has been grown by the Czochralski method. The optical spectra of (Cr4+,Nd3+)∶Gd3Ga5O12 single crystals with 2at.% Nd and different Cr4+ concentrations were measured. The effect of Cr concentrations on, fluorescence lifetime and fluorescence peak wavelength of (Cr,Nd)∶GGG crystals were analyzed. The absorption spectra of Cr4+∶GGG, Nd3+∶GGG and (Cr4+,Nd3+)∶GGG crystal are compared. The fluorescent lifetime of (Cr4+,Nd3+)∶GGG and Nd3+∶GGG are 33 μs and 240 μs, respectively. This crystal may be potential materials for compact, efficient, high stability laser-diode-pumped passive Q-switched solid-state laser.