The electric field gradient (EFG) tensor at the aluminum nucleus sites in yttrium-aluminum garnet Y₃Al₅O₁₂ is calculated using the Hartree-Fock method and the nonempirical cluster approach. It is shown that the EFG tensor at the Al_tetr sites is described well taking into account the nearest neighbors (an [AlO₄]^-5 cluster), whereas for the Al_oct sites the effect of more distant ions is important. The results are compared with the available experimental data and the results of band calculations.