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 Hunds 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 $langle S_i^zS_{i+1}^zrangle>0$ and an intermediate left-left-right-right phase with $langle S_i^xS_{i+1}^xrangle eq 0$. A~quantum spin liquid is stable near the Kitaev limit, while a topological Haldane phase is found for $J>0$.
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