The electronic structure and magnetism of eskolaite are studied by using first-principles calculations where the on-site Coulomb interaction and the exchange interaction are taken into account and the LSDA+U method is used.The calculated energies of magnetic configurations are very well fitted by the Heisenberg Hamiltonian with interactions in five neighbour shells; interaction with two nearest neighbours is found to be dominant. The Neel temperature is calculated in the spin-3/2 pair-cluster approximation. It is found that the measurements are in good agreement with for the values of U and J that are close to those obtained within the constrained occupation method.The band gap is of the Mott-Hubbard type.