The light source contains a gas filled chamber with a region of radiating plasma sustained by a focused beam of a CW laser. The means for plasma ignition is a pulsed laser system generating a first and a second laser beams focused in the chamber. The first laser beam provides the optical breakdown, after which the second laser beam ignites the plasma, whose volume and density are sufficient for stationary plasma sustenance by CW laser after finishing the second laser pulse. Preferably, the first laser beam is generated in Q-switching mode and the second laser beam is generated in free-running mode. The technical result consists in ensuring high reliability of igniting the plasma, in creating in this basis electrodeless high-brightness broadband light sources with the high spatial and power stability, and in providing an ability to collect broadband plasma radiation in a spatial angle of more than 9 sr.