Development of laser technologies increases requirements for lasers being developed which generate narrow-band radiation at different wavelengths. In view of this, the importance of wavelength-tunable diode and vibronic lasers with broadband amplification circuits increases. A possibility of generating highly coherent radiation in a solid-state alexandrite laser using an original composite cavity which includes an additional external dispersive cavity is confirmed. Conditions for narrow-band (less than 20 pm) radiation generation in this cavity with a possibility of smooth tuning the lasing wavelength in the spectral range 740–780 nm are experimentally studied. Narrow-band lasing in an alexandrite laser with a radiation energy of 30 mJ and a pulse duration of 35 ns is shown. The created compact narrow-band alexandrite laser can be an effective alternative to parametric oscillators (OPO) and Ti:Sapphire lasers in lidar systems operating in the spectral range 700–850 nm.