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 Néel temperature is calculated in the spin-3/2 pair-cluster approximation. It is found that the measurements are in good agreement with the calculations of lattice parameters, density of states, band gap, local magnetic moment, and the Néel temperature 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.