  Using the complete numerical solution of a time-dependent three-dimensional
mean-field model we study the Josephson oscillation of a superfluid Fermi gas
(SFG) at zero temperature formed in a combined axially-symmetric harmonic plus
one-dimensional periodic optical-lattice (OL) potentials after displacing the
harmonic trap along the axial OL axis. We study the dependence of Josephson
frequency on the strength of the OL potential. The Josephson frequency
decreases with increasing strength as found in the experiment of Cataliotti et
al. [Science 293 (2001) 843] for a Bose-Einstein condensate and of the
experiment of Pezze et al. [Phys. Rev. Lett. 93 (2004) 120401] for an ideal
Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a
large displacement of the harmonic trap. These features of Josephson
oscillation of a SFG can be tested experimentally.
