WE studied the growth of GaInNAs crystal by solid-source molecular beam epitaxy in which the solid As was used as As source. Since solid As supply is not limited by the pumping capacity (unlike AsH3), we could widely vary the growth conditions, such as the V/III ratio and growth rate. We found that a V/III ratio higher than 5.0 and a growth rate higher than 2.25 mum/h were effective for improving the crystal quality of GaInNAs. By optimizing the growth conditions and applying thermal annealing, we were able to grow GaInNAs that had crystal quality comparable with that of conventional III-V semiconductor materials, such as GaInAs. Therefore, the use of solid As could greatly improve the crystal quality of GaInNAs. Moreover, by using this growth method, we can grow GaInNAs without hydrogen atoms. Since the variation of photoluminescence characteristics of GaInNAs resulting from thermal annealing is similar to that observed in GaInNAs with hydrogen atoms, we concluded that the incorporation of hydrogen atoms was not the primary cause of the poor crystallinity of as-grown GaInNAs. These results should bring about further improvement of laser performance in GaInNAs laser diodes.