We investigate the steady-state phase diagram of the dissipative spin-1/2 XYZ model on a two-dimensional triangular lattice, in which each site is coupled to a local environment. By means of cluster mean-field approximation, we find that the steady-state phases of the system are rather rich, in particular there exist various types of nonuniform antiferromagnetic phases due to the geometrical frustration. As the short-range correlations included in the analysis, the numerical results show that the oscillatory phase disappears while the triantiferromagnetic and biantiferromagnetic phases remain to exist in the thermodynamic limit. Moreover, the existence of the spin-density-wave phase, which is missed by the single-site mean-field analysis, is also revealed by the spin-structure factor.
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