High-quality CuInSe2 single crystals were studied using polarization resolved photoluminescence (PL) and magnetophotoluminescence (MPL). The emission lines related to the first (n=2) excited states for the A and B free excitons were observed in the PL and MPL spectra at 1.0481 meV and 1.0516 meV, respectively. The spectral positions of these lines were used to estimate accurate values for the A and B exciton binding energies (8.5 meV and 8.4 meV, respectively), Bohr radii (7.5 nm), band gaps (E-g(A)=1.050 eV and E-g(B)=1.054 eV), and the static dielectric constant (11.3) assuming the hydrogenic model