  We have investigated quantum entropy of a static black hole arising from the
massless scalar field with Lorentz violation induced by the coupling to
Einstein tensor. Our results show that the coupled massless scalar field
contributes to the classical Bekenstein-Hawking term in the black hole entropy.
The corrected classical Bekenstein-Hawking entropy is not one quarter of the
event horizon area of the original background black hole, but of a
corresponding effective metric related to the coupling. It means that the
classical Bekenstein-Hawking entropy depends not only on the black hole
parameter, but also on the coupling which reduces Lorentz violation.
