The X-ray binary Her X-1 consists of an accreting neutron star and the optical companion HZ Her. The 35-day X-ray variability of this system is known since its discovery in 1972 by the UHURU satellite and is believed to be caused by forced precession of the warped accretion disk tilted to the orbital plane. We argue that the observed features of the optical variability of HZ Her can be explained by free precession of the neutron star with a period close to that of the forced disk precession. The model parameters include a) the intensity (power) of the stream of matter flowing out of the optical star; b) the X-ray luminosity of the neutron star; c) the optical flux of the accretion disk; d) the X-ray irradiation pattern on the donor star; e) the tilt of the inner and outer edge of the accretion disk. A possible synchronization mechanism based on the coupling between the neutron star free precession and the dynamical action of non-stationary gas streams is discussed shortly.