  We apply the membrane paradigm and the holographic Wilsonian approach to the
Einstein-Gauss-Bonnet-Maxwell theory. The transport coefficients for a
quark-gluon plasma living on the cutoff surface are derived in a spacetime of
charged black brane. Because of the mixing of the Gauss-Bonnet coupling and the
Maxwell fields, the vector modes/shear modes of the metric and Maxwell
fluctuations turn out to be very difficult to decouple. We firstly evaluate the
AC conductivity at a finite cutoff surface by solving the equation of motion
numerically, then manage to derive the radial flow of DC conductivity with the
use of the Kubo formula. It turns out that our analytical results match the
numerical data in low frequency limit very well. The diffusion constant
$D(u_c)$ is also derived in a long wavelength expansion limit. We find it
depends on the Gauss-Bonnet coupling as well as the position of the cutoff
surface.
