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We extend the work of An, Guan and Kleinbock on bounded orbits ofdiagonalizable flows on $\mathrm{SL}_3(\mathbb{R})/\mathrm{SL}_3(\mathbb{Z})$to $\mathrm{SL}_3(\mathbb{C})/\mathrm{SL}_3(\mathcal{O}_{\mathbb{K}})$, where$\mathbb{K}$ is an imaginary quadratic field. This is achieved by setting anappropriate Schmidt game in $\mathbb{C}^3$ such that bounded orbits correspondto a hyperplane-absolute-winning set consisting of certain vectors in$\mathbb{C}^3$ relative to an approximation by imaginary quadratic rationals in$\mathbb{K}$.

Hyperplane absolute winning property of bounded orbits under  diagonalizable flows on  $\mathrm{SL}_3(\mathbb{C})/\mathrm{SL}_3(\mathcal{O}_{\mathbb{K}})$