With the help of time resolved magneto-optic Kerr rotation measurements， the optically induced spin precession in heavily doped diluted magnetic semiconductor Ga0.937Mn0.063As was observed. It was found that the effective g factor increases with increasing magnetic field， which is attributed to the magnetic-field-induced increase of the density of the non-localized holes. Those free holes will couple with the localized magnetic ions by p-d interactions， leading to the formation of spontaneous magnetization in Ga0.937Mn0.063As， which in turn to the enhancement of the effective g factor.