  We present a theoretical study on the electron transmission through the AB-BA
stacking boundary in multilayer graphene. Using the tight-binding model and the
transfer matrix method, we calculate the electron transmission probability
through the boundary as a function of electron Fermi energy in multilayers from
bilayer to five-layer. We find that the transmission is strongly suppressed
particularly near the band touching point, suggesting that the electronic
conductivity in general multilayer graphenes is significantly interfered by
stacking fault. The conductivity suppression by stacking fault is the strongest
in the bilayer graphene, while it is gradually relaxed as increasing the number
of layers. At a large carrier density, we observe an even-odd effect where the
transmission is relatively lower in trilayer and five-layer than in bilayer and
four-layer, and this is related to the existence of a monolayer-like linear
band in odd layers. For bilayer graphene, we also study the effect of the
perpendicular electric field opening an energy gap, and show that the band
deformation enhances the electron transmission at a fixed carrier density.
