We report on band structure calculations and a microscopic model of the low-dimensional magnet β-Cu2V2O7. Magnetic properties of this compound can be described by a spin-1 2 anisotropic honeycomb lattice model with the averaged couplingJ1 = 60 − 66 K. The low symmetry of the crystal structure leads to two inequivalent couplings J1 and J ′ 1 , but this weak spatial anisotropy does not affect the essential physics of the honeycomb spin lattice. The structural realization of the honeycomb lattice is highly non-trivial: the leading interactions J1 and J ′ 1 run via double bridges of VO4 tetrahedra between spatially separated Cu atoms, while the interactions between structural nearest neighbors are negligible. The non-negligible inter-plane coupling J ⊥ ≃ 15 K gives rise to the long-range magnetic ordering at TN ≃ 26 K. Our model simulations improve the fit of the magnetic susceptibility data, compared to the previously assumed spin-chain models. Additionally, the simulated ordering temperature of 27 K is in remarkable agreement with the experiment. Our study evaluates β-Cu2V2O7 as the best available experimental realization of the spin-1 2 Heisenberg model on the honeycomb lattice. We also provide an instructive comparison of different band structure codes and computational approaches to the evaluation of exchange couplings in magnetic insulators.