A chromium‐ and neodymium‐codoped gadolinium scandium gallium garnet (Cr:Nd:GSGG) crystal was tested for pulsed‐ and continuous‐wave (cw) laser operations with a flashlamp and solar simulator as pumping sources. The crystal has been considered as a good candidate for a solar‐pumped laser because of its broad absorption bands over the solar spectrum. However, it was observed experimentally and theoretically that its cw laser operation is difficult at high pump powers because too many thermal lensing effects are induced. Only at low solar‐simulator beam intensities of up to 1500 solar constants (203 W/cm2) was cw laser operation lasting longer than 10 min achieved. For higher pump beam intensities of up to 2500 solar constants (338 W/cm2), a quasi‐cw‐laser operation was obtained with continuously chopped pumping with a duty cycle of 0.5 and a repetition rate of 13 Hz. The experimental result was compared with the calculated stability condition of the laser resonator for various pump powers and showed that the thermal focusing of the Cr:Nd:GSGG is 15–8 times greater than that of the neodymium‐doped yttrium aluminum garnet (Nd:YAG) laser for the pump beam intensities from 1000 to 3000 solar constants.