The spectral oscillation of intrinsic photoconductivity in GaSb has been studied under applied magnetic fields. There is a shift of the minima to higher photon energies corresponding to an increase of the energy gap under a magnetic field. More strikingly, additional structures appear in the spectrum. The oscillation is more pronounced with longitudinal magnetic fields than with transverse fields. The spectrum is interpreted by considering transitions between Landau bands of the conduction band and those of the valence band. Under a longitudinal field, a minimum in photoconductivity may occur when the energy of photoexcited electrons, after the emsision of LO phonons if the initial energy is sufficiently high, is close to a Landau level. As expected, the oscillation is weaker under a transverse field and may even appear to be reversed.