A tunable, lamp-pumped Cr3+:LiCaAlF6 laser that operates in the 760-800-nm wavelength range is demonstrated. As a passive Q switch the V3+:YAG crystal, characterized by wide saturable absorption in the 760-900-nm wavelength range, was applied. The V3+:YAG parameters were determined by spectroscopic and saturable transmission measurements. The 30-mJ output energy at 2-Hz repetition rate in the free-running regime was obtained in a cavity reinforced by a diaphragm near the fundamental mode. The dispersive prism inserted into the cavity enabled tuning in the 760-800-nm wavelength range. In the passive Q-switching regime we achieved greater than 1-mJ energy with 50-ns pulse duration in a 35-cm-long cavity. A numerical model that takes into account the short recovery time of V3+:YAG (approximately 5 ns) and excited-state absorption was used to analyze such a laser.