  Information geometry is the application of differential geometry in
statistics, where the Fisher-Rao metric serves as the Riemannian metric on the
statistical manifold, providing an intrinsic property for parameter
sensitivity. In this paper, we explore the Fisher-Rao metric with the
non-Hermitian systems. By approximating the Lindblad master equation in the
non-Hermitian Hamiltonian, we calculate the time evolution of the quantum
geometric metric. Finally, we give an example of the quantum spin Ising model
of the imaginary magnetic field, explore the energy spectrum of
$\mathcal{PT}$-symmetric Hamiltonian and the evolution of geometric metric, and
discuss that the dissipative effect of the imaginary magnetic field can be
eliminated under the condition of adding the control Hamiltonian, so as to
improve the accuracy of parameter estimation.
