  The quantum Fisher information constrains the achievable precision in
parameter estimation via the quantum Cram\'er-Rao bound, which has attracted
much attention in Hermitian systems since the 60s of the last century. However,
less attention has been paid to non-Hermitian systems. In this Letter, working
with different logarithmic operators, we derive two previously unknown
expressions for quantum Fisher information, and two Cram\'er-Rao bounds lower
than the well-known one are found for non-Hermitian systems. These lower bounds
are due to the merit of non-Hermitian observable and it can be understood as a
result of extended regimes of optimization. Two experimentally feasible
examples are presented to illustrate the theory, saturation of these bounds and
estimation precisions beyond the Heisenberg limit are predicted and discussed.
A setup to measure non-Hermitian observable is also proposed.
