  We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a
two-dimensional honeycomb lattice numerically by density matrix renormalization
group method. By tuning the relative value of the Kitaev and Heisenberg
exchange couplings, we obtain the whole phase diagram with two spin liquid
phases and four symmetry broken phases. We identify that the spin liquid phases
are gapless by calculating the central charge at the pure Kitaev points without
Heisenberg interaction. Comparing to its spin-1/2 counterpart, the position and
number of gapless modes of the spin-1 case are quite different. Due to the
approximate $Z_2$ local conservations, the expectation value of Wilson loop
operator measuring the flux of each plaquette stays near to 1, and the static
spin-spin correlations remain short-range in the entire spin liquid phases.
