The invention discloses a gadolinium yttrium scandium gallium garnet crystal (GYSGG) and a crystal growth method by a melt method thereof. The molecular formula of the crystal can be expressed as Gd3xY3(1-x)Sc2Ga3(1+delta)O12 (the x is equal to between 0 and 1 or between -0.2 and 0.2); Gd2O3, Y2O3, Sc2O3 and Ga2O3, or corresponding other compounds of gadolinium, yttrium, scandium, and gallium canbe used to perform the material mixing, and the premise is that the Gd3xY3(1-x)Sc2Ga3(1+delta)O12 is produced; prepared raw materials are subject to the perfect mixing, press forming and high temperature sintering, and then become an initial raw material of crystal growth; the initial raw material of the growth is placed into a crucible, is heated to fully melt down, and then becomes an initial melt of the growth by the melt method, and then melt methods such as a pulling method, a crucible descending method or a temperature gradient method as well as other melt methods can be used for the growth; for the melt method which needs seed crystals to directionally grow, the seed crystals are GYSGG monocrystals or yttrium scandium gallium garnet (YSGG) monocrystals or gadolinium scandium gallium garnet (GSGG) monocrystals. The GYSGG monocrystals can be used as a substrate material of a Bi3+-doped yttrium iron garnet epitaxial film.