The ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are studied. By using of the double-time Green's function method within the Tyablikov decoupling for the exchange anisotropy and Callen's approximation for the single-ion anisotropy, the Neel temperature, magnetization and susceptibility are investigated. Their relations with the temperature and anisotropic parameter are analyzed over the entire range of temperature. It is found that our results agree well with spin wave theory results at low temperature, agree with the high temperature series results at high temperature, and compare reasonably well with the linked-cluster series approach and ratio method results at intermediate temperature.
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