The optimum growth condition of GaInNAs/GaAs quantum wells (QWs) by plasma-assisted molecular beam epitaxy was investigated. High-resolution X-ray diffraction and photoluminescence (PL) measurements showed that ion damage drastically degraded the quality of GaNAs and GaInNAs QWs and that ion removal magnets can effectively remove the excess ion damage. Remarkable improvement of PL intensity and obvious appearance of pendellosung fringes were observed by removing the N ions produced in the plasma cell. When the growth rate increased from 0.73 to 1.2 ML/s, the optimum growth temperature was raised from 460 degreesC to 480 degreesC and PL peak intensity increased two times. Although the N composition decreased with increasing growth rate, degradation of optical properties of GaInNAs QWs was observed when the growth rate was over 0.92 ML/s. Due to low-temperature growth of GaInNAs QWs, a distinctive reflection high-energy electron diffraction pattern was observed only when the GaAs barrier was grown under lower As-4 pressure. The samples with GaAs barriers grown under lower As-4 pressure (V/III ratio about 24) exhibited seven times increase in PL peak intensity compared with those grown under higher As-4 pressure (V/III ratio about 50).