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The spontaneous magnetization of the Ho3+ ion in holmium iron gaet (HoIG) single crystals in the temperature range of 4.2-294K along the directions [111],[110],and [100] are calculated,taking into account the effects of six magnetically inequivalent sites occupied by the Ho3+ ions based on the quantum theory.The calculated results show that the magnetization of the Ho3+ ion in HoIG is obviously anisotropic.The theoretical results are in agreement with those of experiments.A primary interpretation of the anisotropy of magnetization of the Ho3+ ion in HoIG is put forward.