  We propose a method of computing and studying entanglement quantities in
non-Hermitian systems by use of a biorthogonal basis. We find that the
entanglement spectrum characterizes the topological properties in terms of the
existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH)
model with parity and time-reversal symmetry (PT symmetry) and the
non-Hermitian Chern insulators. In addition, we find that at a critical point
in the PT symmetric SSH model, the entanglement entropy has a logarithmic
scaling with corresponding central charge $c=-2$. This critical point then is a
free-fermion lattice realization of the non-unitary conformal field theory.
