We have observed infrared absorption due to residual Li accepters in bulk ZnSe. From the experimental results, we 2.58 and have estimated the Luttinger parameters gamma(1), gamma(2) and gamma(3), which characterize the valence band structure, to be 6.44, 2.58 and 2.74, respectively. In addition, distorted structures in the absorption spectra due to Fano resonances between LO-phonon-coupled excited states and the valence band states, have been found above the ionization energy of the Li acceptor.