Boron nitride films with different cubic phase contents were deposited in a radio frequency bias sputtering system by a two-stage deposition process. The Fourier transform infrared spectra and UV-visible transmittance and reflection spectra were measured. The optical absorption edge of BN films consists of a low energy region in which a increases exponentially as incident photon energy hn, and a high energy region, in which a varies as (hn)m, which is the characteristics of amorphous materials. These two regions are fitted by the Urbach tail model and the band-to-band transition model with an effective medium approach, and the Urbach energy and the optical band gap are determined from these fits. With an increase in the cubic boron nitride (c-BN) content, the absorption edge shifts to the higher energy and the optical band gap increases. For a BN film with 88% cubic phase, the optical band gap exceeds 6.0 eV, which is comparable to that of c-BN single crystal.