  We develop the perturbation theory of the fidelity susceptibility in
biorthogonal bases for arbitrary interacting non-Hermitian many-body systems
with real eigenvalues. The quantum criticality in the non-Hermitian transverse
field Ising chain is investigated by the second derivative of ground-state
energy and the ground-state fidelity susceptibility. We show that the system
undergoes a second-order phase transition with the Ising universal class by
numerically computing the critical points and the critical exponents from the
finite-size scaling theory. Interestingly, our results indicate that the
biorthogonal quantum phase transitions are described by the biorthogonal
fidelity susceptibility instead of the conventional fidelity susceptibility.
