  We investigate the ground state properties of the spin S=1 Kitaev honeycomb
model under a magnetic field based on the density matrix renormalization group
(DMRG) calculation. With the time reversal symmetry breaking due to the
magnetic field, a gapped Kitaev spin liquid is identified for both
ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev couplings. The
topological nature of such Kitaev spin liquid is manifested by the nearly
quantized Wilson loop, degeneracy in the entanglement spectra and existence of
edge modes. While the FM Kitaev spin liquid is destroyed by a weaker magnetic
field $H_*^\text{FM}$, the AFM one demonstrates a robustness up to an order of
magnitude larger critical field $H_*^\text{AFM}$. Moreover, an intermediate
nonmagnetic phase appears only for the AFM case at larger fields,
$H_*^\text{AFM} < H < H_{**}^\text{AFM}$, before the transition to a high-field
polarized paramagnet. The stability of the Kitaev spin liquid against the
Heisenberg interactions is also examined. Our findings may further inspire the
investigation of recently proposed S=1 Kitaev materials.
