  To clarify a key role of $f$ orbitals in the emergence of
antiferro-quadrupole structure in PrPb$_{3}$, we investigate the ground-state
property of an orbital-degenerate Kondo lattice model by numerical
diagonalization techniques. In PrPb$_{3}$, Pr$^{3+}$ has a $4f^{2}$
configuration and the crystalline-electric-field ground state is a non-Kramers
doublet $\Gamma_{3}$. In a $j$-$j$ coupling scheme, the $\Gamma_{3}$ state is
described by two local singlets, each of which consists of two $f$ electrons
with one in $\Gamma_{7}$ and another in $\Gamma_{8}$ orbitals. Since in a cubic
structure, $\Gamma_{7}$ has localized nature, while $\Gamma_{8}$ orbitals are
rather itinerant, we propose the orbital-degenerate Kondo lattice model for an
effective Hamiltonian of PrPb$_{3}$. We show that an antiferro-orbital state is
favored by the so-called double-exchange mechanism which is characteristic of
multi-orbital systems.
