Crystal growth of GaN by the pressure-controlled solution growth (PC-SG) method has been carried out using a high-pressure furnace. We have investigated the effect of the supersaturation of nitrogen atoms (the rate of increase of nitrogen pressure) in order to grow large GaN single crystals. It was found that the rate of increase of nitrogen pressure affected the size of a GaN single crystal and its morphology. GaN single crystals with a surface area of about 120 mm(2) and/or with good morphology were obtained at a rate less than 49 MPa/h. We have studied the effect of the supersaturation of nitrogen atoms on the crystallinity. The GaN single crystals obtained had the following good crystallinity: (I) the FWHM of the rocking curve was about 120 arcsec without any low-angle grain; boundaries, (2) the dislocation density was estimated to be less than 10(5)cm(-2) by TEM observations, and (3) the photoluminescence intensity of the yellowish band became very weak and the PL intensity ratio of the band-edge band to the yellowish band was greatly improved. These results clearly suggest that the rate of increase bf the nitrogen pressure in the PC-SG method must be lower to grow large GaN single crystals with good crystallinity.