A GaN single crystal having a full width at half-maximum of the double-crystal X-ray rocking curve of 5-250 sec and a thickness of not less than 80 µm, a method for producing the GaN single crystal having superior quality and sufficient thickness permitting its use as a substrate and a semiconductor light emitting element having high luminance and high reliability, comprising, as a substrate, the GaN single crystal having superior quality and/or sufficient thickness permitting its use as a substrate.