  We study the ferminoic spectrum with Weyl correction, which exhibits the
non-Fermi liquid behavior. Also, we find that both the height of the peak of
the fermionic spectrum and the dispersion relation exhibit a nonlinearity with
the variety of the Weyl coupling parameter $\gamma$, which mean that such
nonlinearity maybe ascribe to the one of the Maxwell field. Another important
property of this system is that for the holographic fermionic system with
$\gamma<0$, the degree of the deviation from Fermi liquid is heavier than that
for the one with $\gamma>0$. It indicates that there is a transition of
coupling strength in the dual boundary field theory.
