  Centaurus A (Cen~A) is the nearest active radio galaxy, which has kiloparsec
(kpc) scale jets and {giant lobes detected by various instruments in radio and
X-ray frequency ranges}. The $Fermi$--Large Area Telescope and High Energy
Stereoscopic System (HESS) confirmed, that Cen~A is a very high-energy (VHE; $>
0.1$~TeV) $\gamma$-ray emitter with a known spectral {softening} in the energy
range from a few GeV to TeV. In this work, we consider a synchrotron
self-Compton model in the nucleus for the broad band spectrum {below the break
energy} and an external Compton model in kpc-scale jets for the $\gamma$-ray
excess. Our results show that the observed $\gamma$-ray excess can be suitably
described by the inverse Compton scattering of the starlight photons in the
kpc-scale jets, which is consistent with the recent tentative report by the
HESS on the spatial extension of the TeV emission along the jets. Considering
the spectral fitting results, the excess can only be seen in Cen~A, which is
probably due to two factors: (1) the host galaxy is approximately 50 times more
luminous than other typical radio galaxies and (2) the core $\gamma$-ray
spectrum quickly decays above a few MeV due to the low maximum electron Lorentz
factor of $\gamma_{\rm c}=2.8 \times 10^3$ resulting from the large magnetic
field of 3.8~G in the core. By the comparison with other $\gamma$-ray detected
radio galaxies, we found that the magnetic field strength of relativistic jets
scales with the distance from the central black holes $d$ with $B (d) \propto
d^{-0.88 \pm 0.14}$.
