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The roles of the exchange interaction between different magnetic ions in the gadolinium gallium gaet Gd3Ga5O12 are systematically investigated.The effective field based on the exchange interaction is expressed as functions of the temperature T and applied field He.Furthermore,the effects of T and He on the magnetic moment and the entropy of Gd3Ga5O12 are studied in the ranges of 0 ＜ He ＜ 9 T and 3 ＜ T ＜ 40K.The computational results are consistent with the experimental data.Our study reveals that the applied field and temperature have important influences on the exchange interaction of Gd3 Ga5 O12 at low temperature.