We numerically investigated the characteristics of diode-end-pumped passively Q-switched solid-state Cr3+:LiSAF lasers. A Cr4+:YSO crystal is used as an intra-cavity saturable absorber. Our obtained results indicate the influences of resonator and pumping parameters on the characteristics of passively Q-switched solid-state Cr3+:LiSAF laser. Particularly, our numerical investigations are done in respect to the Cr3+:LiSAF laser medium of a very wide gain spectrum from 700 nm to 920 nm. Using a CW diode pumping at 670 nm and a Cr3+:LiSAF crystal of 3 mm long and 1 at.%, a stable generation of Q-switching nanosecond Cr3+:LiSAF laser pulse at 850 nm is obtainable with a pulse energy of about 2 mili-joule.