We apply a method that combines the tight-binding approximation and the Löwdin down-folding procedure to evaluate the electronic band structure of the newly discovered pressure-induced superconductor CrAs. By integrating out all low-lying arsenic degrees of freedom, we derive an effective Hamiltonian model describing the Cr d bands near the Fermi level. We calculate and make predictions for the energy spectra, the Fermi surface, the density of states and transport and magnetic properties of this compound. Our results are consistent with local-density approximation calculations and they also show good agreement with available experimental data for resistivity and the Cr magnetic moment.