  By introducing a specific etheric-like vector in the Dirac equation with
Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method
for quantum tunneling radiation of fermions is proposed. As an example, we
apply this new method to a charged axisymmetric Kerr-Newman black hole.
Firstly, considering LIV theory, we derive a modified dynamical equation of
fermion with spin 1/2 in the Kerr-Newman black hole spacetime. Then we solve
the equation and find the increase or decrease of black hole's Hawking
temperature and entropy are related to constants $a$ and $c$ of the Dirac
equation with LIV in the curved spacetime. As $c$ is positive, the new Hawking
temperature is about $ \frac{\sqrt{1+2a+2cmk_r^2}}{\sqrt{1+2a}}$ times higher
than that without modification, but the entropy will decrease. We also make a
brief discussion for the case of high spin fermions.
