  We generalize the vertex expansion approach of the functional renormalization
group to non-Hermitian systems. As certain anomalous expectation values might
not vanish, additional terms as compared to the Hermitian case can appear in
the flow equations. We investigate the merits and shortcomings of the vertex
expansion for non-Hermitian systems by considering an exactly solvable
$\mathcal{PT}$-symmetric non-linear toy-model and reveal, that in this model,
the fidelity of the vertex expansion in a perturbatively motivated truncation
schema is comparable with that of the Hermitian case. The vertex expansion
appears to be a viable method for studying correlation effects in non-Hermitian
systems.
