Anisotropy of the valence band is experimentally demonstrated in CuInSe2, a key component of the absorber layer in one of the leading thin-film solar cell technology. By changing the orientation of applied magnetic fields with respect to the crystal lattice, we measure considerable differences in the diamagnetic shifts and effective g-factors for the A and B free excitons. The resulting free exciton reduced masses are combined with a perturbation model for non-degenerate independent excitons and theoretical dielectric constants to provide the anisotropic effective hole masses, revealing anisotropies of 5.5 (4.2) for the A (B) valence bands.