The crystal field (CF)- and external magnetic field- split ground state of Dy3+ in Dy3Al5O12 (DyAG) has been calculated based on the quantum theory in this paper. The eight CF-split levels are obtained, which are all twofold degenerates and are removed by the external magnetic field. On the basis of the results, the magnetic moments and the magnetic entropy changes of DyAG are calculated in the temperature range of 3 < T < 42 K and the magnetic field range of 0 < H-e < 9 T. The calculated results are in good agreement with the measured data. This work shows that all of the six nonequivalent crystal sites in DyAG have contribution to the average magnetic moment and have an important impact on the magnetic anisotropy of the crystal. In addition, the study indicates that the exchange interaction between the magnetic ions in DyAG is so weak that it may be neglected. However, distinct from DyAG, the exchange interaction between the rare-earth ions in Gd3Ga5O12(GdGG) is stronger at low temperatures and dependent on the temperature and external magnetic field. Besides, the variation of the adiabatic temperature change Delta T with T is theoretically anticipated and the anticipated results are comparied with that of GdGG. It is found that the maximum adiabatic temperature change Delta T of DyAG is 1.27 times larger than that of GdGG when T = 11 K and H-e = 1 T. However, it changes to 1.15 times that of GdGG when T = 16 K and H-e = 2 T. There are differences between the refrigerative properties of DyAG and GdGG when they are in different external magnetic fields and different temperature regions. At low temperature s(T < 10 K), the DyAG is a good magnetic refrigerative material in the lower external magnetic field. However, When H-e is higher, GdGG is a good selection. This study is helpful to select suitable materials for the magnetic refrigeration technology.