  We derive the eikonal equation of light wavefront in the presence of Lorentz
invariance violation (LIV) from the photon sector of the standard model
extension (SME). The results obtained from the equations of $\mathbf{E}$ and
$\mathbf{B}$ fields respectively are the same. This guarantees the
self-consistency of our derivation. We adopt a simple case with only one
non-zero LIV parameter as an illustration, from which we find two points. One
is that, in analogy with Hamilton-Jacobi equation, from the eikonal equation,
we can derive dispersion relations which are compatible with results obtained
from other approaches. The other is that, the wavefront velocity is the same as
the group velocity, as well as the energy flow velocity. If further we define
the signal velocity $v_s$ as the front velocity, there always exists a mode
with $v_s>1$, hence causality is violated classically. Thus our method might be
useful in the analysis of Lorentz violation in QED in terms of classical
causality .
