  Usually duality process keeps energy spectrum invariant. In this paper, we
provide a duality, which keeps entanglement spectrum invariant, in order to
diagnose quantum entanglement of non-Hermitian non-interacting fermionic
systems. We limit our attention to non-Hermitian systems with a complete set of
biorthonormal eigenvectors and an entirely real energy spectrum. The original
system has a reduced density matrix $\rho_\mathrm{o}$ and the real space is
partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After
dualization, we obtain a new reduced density matrix $\rho_{\mathrm{d}}$ and a
new real space projector $\mathcal{R}_{\mathrm d}$. Remarkably, entanglement
spectrum and entanglement entropy keep invariant. Inspired by the duality, we
defined two types of non-Hermitian models, upon $\mathcal R_{\mathrm{o}}$ is
given. In type-I exemplified by the ``non-reciprocal model'', there exists at
least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other words,
entanglement information of type-I non-Hermitian models with a given
$\mathcal{R}_{\mathrm{o}}$ is entirely controlled by Hermitian models with
$\mathcal{R}_{\mathrm{d}}$. As a result, we are allowed to apply known results
of Hermitian systems to efficiently obtain entanglement properties of type-I
models. On the other hand, the duals of type-II models, exemplified by
``non-Hermitian Su-Schrieffer-Heeger model'', are always non-Hermitian. For the
practical purpose, the duality provides a potentially \textit{efficient}
computation route to entanglement of non-Hermitian systems. Via connecting
different models, the duality also sheds lights on either trivial or nontrivial
role of non-Hermiticity played in quantum entanglement, paving the way to
potentially systematic classification and characterization of non-Hermitian
systems from the entanglement perspective.
