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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 a Kitaev spin liquid is manifested by a nearly quantized Wilson loop, degeneracy in the entanglement spectra, and the existence of edge modes. While the FM Kitaev spin liquid is destroyed by a weaker magnetic field H_{*}^{FM}, the AFM one demonstrates a robustness up to an order of magnitude larger critical field H_{*}^{AFM}. Moreover, an intermediate nonmagnetic phase appears only for the AFM case at larger fields, H_{*}^{AFM}<H<H_{**}^{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.