  Recently, it has been proposed that higher-spin analogues of the Kitaev
interactions $K>0$ may also occur in a number of materials with strong Hund's
and spin-orbit coupling. In this work, we use Lanczos diagonalization and
density matrix renormalization group methods to investigate numerically the
$S=1$ Kitaev-Heisenberg model. The ground-state phase diagram and quantum phase
transitions are investigated by employing local and nonlocal spin correlations.
We identified two ordered phases at negative Heisenberg coupling $J<0$:
a~ferromagnetic phase with $\langle S_i^zS_{i+1}^z\rangle>0$ and an
intermediate left-left-right-right phase with $\langle
S_i^xS_{i+1}^x\rangle\neq 0$. A~quantum spin liquid is stable near the Kitaev
limit, while a topological Haldane phase is found for $J>0$.
