  We investigate magnetic properties in the $S=1$ Kitaev model in the
anisotropic limit. Performing the fourth-order perturbation expansion with
respect to the $x$-bonds, $y$-bonds, and magnetic field, we derive the
effective Hamiltonian, where the low-energy physics should be described by the
free spins with an effective magnetic field. Making use of the exact
diagonalization method for small clusters, we discuss ground-state properties
in the system complementary.
