We measure the absorption recovery time, the ground- and excited-state absorption cross sections of a Cr4+:YAG crystal at 640 nm for the first time. A pump-probe measurement reveals the existence of two recovery times of 26 ns and 5.6 μs. By a Z-scan experiment, the ground- and excited-state absorption cross sections are estimated to be 1.70 - 1.75 × 10(-17) and 0.95 - 1.00 × 10(-17)cm2, respectively. The adequacy of the proposed model and the accuracy of the estimated parameters of the saturable absorber are verified by reproducing the experimentally obtained performance of a passively Q-switched Pr3+:YLF laser with the Cr4+:YAG saturable absorber from rate equation analysis.